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# IGEM:IMPERIAL/2006/project/Oscillator/project browser/Prey Construct/Modelling

(Difference between revisions)
 Revision as of 18:11, 29 October 2006 (view source)← Previous diff Revision as of 21:13, 29 October 2006 (view source)Next diff → Line 26: Line 26: ==Model assumptions and relevance== ==Model assumptions and relevance== - *LuxR is at steady state + *General assumptions on gene expression modelling: - **A good approximation if LuxR gene is left in an active state while cells are growing in medium + ::*Quasi-steady state hypothesis on mRNA expression. - *LuxR and AHL bind in a linear second order fashion + ::*Gene activation can be approximated by Hill equations. - **This is not strictly true as LuxR and AHL bind using pseudo-Michaelis-Menten kinetics + *Assumptions linked to the quorum sensing: - **Gives a good approximation if LuxR is in excess of AHL (ie not saturated by AHL) + ::*As a first approximation, we assume that luxR and AHL molecules form a heterodimer (even if it has been found that the complex formed is more complicated. This gives a good approximation if LuxR is in excess of AHL (ie not saturated by AHL) but this is unlikely to occur all the time as LuxI levels increase to very high amounts). - ***Unlikely to occur all the time as LuxI levels increase to very high amounts + ::*The concentration of the heterodimer is in equilibrium with the concentration of AHL - *LuxI can be ignored + ::*LuxR is constitutively produced and reaches steady state before AHL production begins. ([LuxR] in the prey can be considered constant.) - **LuxI levels vary throughout, and it is these levels that are directly responsible for AHL production + *LuxI can be ignored: - **This could be a major flaw in the model + ::*LuxI levels vary throughout, and it is these levels that are directly responsible for AHL production (this may account for a flaw in the model) + ::*The degradation rate of luxR and AHL-lactonase is due to the growth dilution which, in this case, is controlled by the chemostat + ::*AHL is diffusing freely throughout the system - ==Model description== - [[image:J37015_Model.JPG]] + ==Model description for growth of prey== + *A [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/Modelling/J37015 full derivation for the growth of the prey] yields the following equation: - [http://openwetware.org/images/1/1c/J37015.xml J37015 SBML File] + *$\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]$ - ==Model variables and parameters== + [[Image:Slide6a.PNG]] + + ==Model variables and parameters for growth of prey== {| border="1" width="100%" {| border="1" width="100%" Line 49: Line 53: !Name !! Description !! Initial Value !! Confidence !! Reference !Name !! Description !! Initial Value !! Confidence !! Reference |- |- - |width="100"|AHL||Starting [AHL], must be >0|| 1 ||Unknown|| links + |width="100"|AHL|| homoserine lactone acting as the prey-molecule || 0 || depends how good is the control of the prey positive feedback. Should be measured. || links |} |} Line 57: Line 61: ! Name !! Description !! Value !! Confidence !! Reference ! Name !! Description !! Value !! Confidence !! Reference |- |- - |width="100"| AHL Degredation || Rate of AHL Degredation || Half-Life = 24 Hours || Known || links + |width="100"| a || maximum synthesis rate of the pLux promoter || to be characterized || to be measured || links |- |- - |width="100"| AHL Vmax|| Maximum rate of production of AHL ||10|| Unknown || links + |width="100"| a0 || dissociation constant || to be characterized || to be measured || links |- |- - |width="100"| AHL Kd || Value at which [Substrate] gives 50% Vmax || 1000 || Unknown|| links + |width="100"| dg || growth dilution due to chemostat wash-out || to be characterized || to be measured || links |} |} + + ==Characterization== + + *We need to characterize the rate of synthesis of AHL. + *To do this we use the [http://openwetware.org/wiki/IGEM:IMPERIAL/2006/project/Oscillator/project_browser/Test_Sensing_Prey_Construct/Modelling predator sensing test construct] which shares the same tetR promoter as the prey.

## Revision as of 21:13, 29 October 2006

Super Parts Molecular Prey-Predator Oscillator
Actual Part
Sub Parts Test Sensing Prey Construct <bbpart>C0261</bbpart> <bbpart>I13401</bbpart>

## Model assumptions and relevance

• General assumptions on gene expression modelling:
• Quasi-steady state hypothesis on mRNA expression.
• Gene activation can be approximated by Hill equations.
• Assumptions linked to the quorum sensing:
• As a first approximation, we assume that luxR and AHL molecules form a heterodimer (even if it has been found that the complex formed is more complicated. This gives a good approximation if LuxR is in excess of AHL (ie not saturated by AHL) but this is unlikely to occur all the time as LuxI levels increase to very high amounts).
• The concentration of the heterodimer is in equilibrium with the concentration of AHL
• LuxR is constitutively produced and reaches steady state before AHL production begins. ([LuxR] in the prey can be considered constant.)
• LuxI can be ignored:
• LuxI levels vary throughout, and it is these levels that are directly responsible for AHL production (this may account for a flaw in the model)
• The degradation rate of luxR and AHL-lactonase is due to the growth dilution which, in this case, is controlled by the chemostat
• AHL is diffusing freely throughout the system

## Model description for growth of prey

• $\frac{d[AHL]}{dt}= \frac{a * [AHL]}{(a0 + [AHL])} - \frac{b * [AiiA] * [AHL]}{(b0 + [AHL])} - gd * [AHL]$

## Model variables and parameters for growth of prey

Name Description Initial Value Confidence Reference Variables AHL homoserine lactone acting as the prey-molecule 0 depends how good is the control of the prey positive feedback. Should be measured. links
 Name Description Value Confidence Reference Parameters a maximum synthesis rate of the pLux promoter to be characterized to be measured links a0 dissociation constant to be characterized to be measured links dg growth dilution due to chemostat wash-out to be characterized to be measured links

## Characterization

• We need to characterize the rate of synthesis of AHL.
• To do this we use the predator sensing test construct which shares the same tetR promoter as the prey.


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By default sample() randomly reorders the elements passed as the first argument. Business needs require you to analyze a sample of data. sample() function takes a sample of the specified size from the elements of x using either with or without replacement. We can use R’s random number generation facilities to verify this result. It is known that the random sample can be created by using sample function in R. If we want to create a random sample with values 0 and 1 only then there are three different ways to pass them inside the sample function − Creating a vector of 0 … The characteristics of output from pseudo-random number generators (such as precision and periodicity) vary widely. As you can see, our random values are almost perfectly normally distributed. In R, we can draw a random sample of size 10 from the numbers 1 to 1000, using the sample function sample (1:1000, 10). If we try this multiple times, we might get different results. There are several more sampling schemes that might be interesting to explore: Regular sampling, skip the randomness and just sample regularly. rn = sample(5:20, 5) rn. The answer depends on what kind of random number you want to generate. The full list of standard distributions available can be seen using ?distribution. The larger the sample size gets, the smoother the normal distribution of our random values will be. The small peaks in the distribution are due to random noise. The sample command instructs R to generate 500 random values and place them in the draws. Note most business analytics datasets are data.frame ( records as rows and variables as columns) in structure or database bound.This is partly due to a legacy of traditional analytics software. Code. تعلم برنامج الآر Learn R Simple Random Sample selection using the "sampling" package. R Language Random permutations Example. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Random Number Generation.Random.seed is an integer vector, containing the random number generator (RNG) state for random number generation in R.It can be saved and restored, but should not be altered by the user. replace=TRUE makes sure that no element occurs twice. Now, use sample to create a random permutation of the vector x.. sample(x) [1] 3 2 1 10 7 9 4 8 6 5 sample_n() function in R Language is used to take random sample specimens from a data frame. This reduces the risk of your model failing in field testing. The ﬁrst argument is the possible x values, while the prob argument speciﬁes their probabilities. The holdout sample is your insurance policy against false insights. Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. We’ll select one value from the histogram according to where the random number falls. 5.3 Generating random data. Output: Generating a random sample of 5 To select a sample R has sample() function. A simple random sample is a subset of a statistical population in which each member of the subset has an equal probability of being chosen. Functions that generate random deviates start with the letter r. That’s the solution, which is already provided with the base installation of R (or RStudio). Just from random chance. References. This tutorial explains how to perform stratified random sampling in R. Example: Stratified Sampling in R. A high school is composed of 400 students who are either Freshman, Sophomores, Juniors, or Seniors. Otherwise x can be any R object for which length and subsetting by integers make sense: S3 or S4 methods for these operations will be dispatched as appropriate. Then, we generate a pseudo-random number from a uniform distribution between 0 and 1. One out of four numbers are 1, the out of four are 3. A tutorial on how to implement the random forest algorithm in R. When the random forest is used for classification and is presented with a new sample, the final prediction is made by taking the majority of the predictions made by each individual decision tree in the forest. Generating random samples from a normal distribution. In order to generate random integers between 5 and 20 below the sample function code is used. R sample Function. sampleRandom: Random sample in raster: Geographic Data Analysis and Modeling rdrr.io Find an R package R language docs Run R in your browser R Notebooks Generating Random Values in R The simple case of generating a uniform random number between 0 and 1 is handled by ... Also, samples from a set of numbers or names can be drawn by the sample function. I recently found myself in need of a function to sample randomly from an arbitrarily defined probability density function. This means that the default size is the size of the passed array. R has functions to generate a random number from many standard distribution like uniform distribution, binomial distribution, normal distribution etc. x: Either a (numeric, complex, character or logical) vector of more than one element from which to choose, or a positive integer. Samples the entire … As a language for statistical analysis, R has a comprehensive library of functions for generating random numbers from various statistical distributions. See Also. A random sample has no garantuees that there will be no clusters, because of its random nature. Random Sampling a Dataset in R A common example in business analytics data is to take a random sample of a very large dataset, to test your analytics code. In its simplest form, the sample function can be used to return a random permutation of a vector. Simple random sampling. Simple random sampling is the most straightforward approach to getting a random sample. The basic idea is to simulate outcomes of the true distribution of $$\overline{Y}$$ by repeatedly drawing random samples of 10 observation from the $$\mathcal{N}(0,1)$$ distribution and computing their respective averages. Random numbers in R. The creation of random numbers, or the random selection of elements in a set (or population), is an important part of statistics and data science. Package ‘random’ February 5, 2017 Version 0.2.6 Date 2017-02-05 Author Dirk Eddelbuettel Maintainer Dirk Eddelbuettel Title True Random Numbers using RANDOM.ORG Description The true random number service provided by the RANDOM.ORG website created by Mads Haahr samples atmospheric noise via radio tuned to Take a random sample from the cell values of a Raster* object (without replacement). sample(x, size, replace = FALSE, prob = NULL) sample.int(n, size = n, replace = FALSE, prob = NULL) x: either a vector of one or more elements from which to choose, or a positive integer n: a positive number, the number of items to choose from Even though we would like to think of our samples as random, it is in fact almost impossible to generate random numbers on a computer. For sample the default for size is the number of items inferred from the first argument, so that sample(x) generates a random permutation of the elements of x (or 1:x). The replace argument is set to TRUE as we want to sample with replacement. The last line uses a weighed random distribution instead of a uniform one. The best way to sample such a histogram is to split the 0–1 interval into subintervals whose width is the same as the probability of the histogram bars. With sample( … ) we specify that we want to use the sample function of Base R. With 1:nrow(data), 3 we specify that we want to select three random values between 1 and the number of rows of our data frame. Generate a random number … An excellent post by Quantitations . By splitting off part of your sample and requiring that any findings replicate within that sample, you reduce the risk of selecting a model build on false trends. A simple random sample is … To generate random permutation of 5 numbers: sample(5) # [1] 4 5 3 1 2 To generate random permutation of any vector: sample(10:15) # [1] 11 15 12 10 14 13 One could also use the package pracma. In this post, I want to focus on the simplest of questions: How do I generate a random number? From simulating coin tosses to selecting potential respondents for a survey, we have a heavy reliance on random number generation. Because R is a language built for statistics, it contains many functions that allow you generate random data – either from a vector of data that you specify (like Heads or Tails from a coin), or from an established probability distribution, like the Normal or Uniform distribution.. It involves picking the desired sample size and selecting observations from a population in such a way that each observation has an equal chance of selection until the desired sample … To illustrate this, let’s create a vector of the integers from 1 to 10 and assign it to a variable x.. x . Wadsworth & Brooks/Cole. To generate random integers built-in sample() function is reliable and quick. Suppose we’d like to take a stratified sample of 40 students such that 10 students from each grade are included in the sample. I don't use R, so I can't say what the mistake is exactly -- but I just coded up your solution (taking care to take the middle root of the cubic polynomial, which always lies between 0 and 1), and I get good agreement between the samples and the expected distribution. shows how to accomplish this using some of Rs fairly sophisticated functional approximation tools such as integrate and uniroot.. Statisticians attempt for the samples to represent the population in question. Let's illustrate by example. If you want to use R’s built in random sampling functionality, a popular option is making use of sample & nrow. See .Random.seed for more information on R 's random number generation algorithms. In statistics, quality assurance, and survey methodology, sampling is the selection of a subset (a statistical sample) of individuals from within a statistical population to estimate characteristics of the whole population. Random Samples and Permutations Description. Arguments size Syntax: sample_n(x, n) Parameters: x: Data Frame n: size/number of items to select Example 1: Usage sample(x, size, replace = FALSE, prob = NULL) Arguments. Version info: Code for this page was tested in R version 3.0.2 (2013-09-25) On: 2013-11-19 With: lattice 0.20-24; foreign 0.8-57; knitr 1.5 1. Figure 1 shows the output of the previous R code. sample takes a sample of the specified size from the elements of x using either with or without replacement. - 1:10 . Like uniform distribution, binomial distribution, normal distribution etc the prob argument speciﬁes their probabilities, the! Between 0 and 1 to select a sample of the specified size the! 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# Partial derivative question

1. Apr 18, 2014

### Doctorchaos

Hello,

Wolfram is giving me the required answer however, the steps it uses I find very confusing. Can anyone share some light on how wolfram achieved the correct answer.

As im new to this site, I wont be using any code. I am in the process of writing it up on Latex.

Here is the link for wolframs partial derivative widget

http://www.wolframalpha.com/widget/...tep solution&showAssumptions=1&showWarnings=1

However it keeps changing my function, if the exponential appears on the bottom, can you please use this function

(((1)\(y)^(0.5))))(e^((-x^2-4y^2)\(4y))) WITH RESPECT TO Y

Thankyou everyone, it might seem like an elementary question. The bit I don't understand though is where it says factor out the constants. Its not the factor out the constants but, but the differentiation inside that subsection. That's my main problem

2. Apr 18, 2014

### Staff: Mentor

What does the expression above have to do with the one you entered into Wolframalpha?
The function you entered into WA was
$$\frac{\sqrt{x}}{e^{\sqrt{x}(y^2 + 4x^2)}}$$

If it's this one -- (((1)\(y)^(0.5))))(e^((-x^2-4y^2)\(4y))) -- the problem we most often run into is the OP using too few parentheses. Here you are using way too many, which makes what you wrote difficult to read.

In a simpler form, it would be (1/y.5)e((-x2 - 4y2)/(4y)

LaTeX can be used for complicated expressions, as below:
$$\frac{1}{y^{1/2}}e^{\frac{-x^2 - 4y^2}{4y}}$$

Last edited: Apr 18, 2014


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Notes On Deforestation - CBSE Class 9 History
Forests form an important part of our ecosystem and are beneficial to us in various ways. The process of clearing of forests by removing trees through logging or burning is called deforestation. Major deforestation in India occurred during the British rule, between the years 1880 and 1920. The British grew many cash crops in India, like indigo, cotton, jute and sugar, to increase revenue. As the demand for these products increased, the need for land also increased. The net result was that forests were cleared for cultivation. Large amounts of timber from Sal and teak forests were exported to build the large and magnificent ships of the Royal Navy of England. With the advent of railways, wood was needed as fuel to run locomotives and also to lay sleepers under railway lines. Tea and coffee plantations were grown to meet Europe’s growing need. The Adivasis and the peasants were also largely responsible for the depletion of forests due to their dependence on them for fodder, leaves and fuel. They followed slash and burn and shifting cultivation, which led to deforestation and degradation of the land. Global warming is just one of the several harmful impacts of deforestation. In addition to this, the water cycle gets disturbed, soil erodes, and several species of plants and animals get extinct. It also has an impact on the native dwellers of forests as they become homeless.

#### Summary

Forests form an important part of our ecosystem and are beneficial to us in various ways. The process of clearing of forests by removing trees through logging or burning is called deforestation. Major deforestation in India occurred during the British rule, between the years 1880 and 1920. The British grew many cash crops in India, like indigo, cotton, jute and sugar, to increase revenue. As the demand for these products increased, the need for land also increased. The net result was that forests were cleared for cultivation. Large amounts of timber from Sal and teak forests were exported to build the large and magnificent ships of the Royal Navy of England. With the advent of railways, wood was needed as fuel to run locomotives and also to lay sleepers under railway lines. Tea and coffee plantations were grown to meet Europe’s growing need. The Adivasis and the peasants were also largely responsible for the depletion of forests due to their dependence on them for fodder, leaves and fuel. They followed slash and burn and shifting cultivation, which led to deforestation and degradation of the land. Global warming is just one of the several harmful impacts of deforestation. In addition to this, the water cycle gets disturbed, soil erodes, and several species of plants and animals get extinct. It also has an impact on the native dwellers of forests as they become homeless.

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## Gallagher, Isabelle

Compute Distance To:
 Author ID: gallagher.isabelle Published as: Gallagher, Isabelle; Gallagher, I. External Links: MGP · Wikidata · GND · IdRef · theses.fr
 Documents Indexed: 96 Publications since 1997, including 3 Books 1 Contribution as Editor Reviewing Activity: 9 Reviews Co-Authors: 40 Co-Authors with 75 Joint Publications 1,176 Co-Co-Authors
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### Co-Authors

 22 single-authored 21 Chemin, Jean-Yves 17 Saint-Raymond, Laure 15 Bahouri, Hajer 8 Bodineau, Thierry 6 Desjardins, Benoît 6 Fermanian-Kammerer, Clotilde 6 Grenier, Emmanuel 6 Planchon, Fabrice 4 Carles, Rémi 3 Gallay, Thierry 3 Paul, Thierry 3 Zhang, Ping 2 Cheverry, Christophe 2 Feireisl, Eduard 2 Gérard-Varet, David 2 Gerard, Patrick 2 Ibrahim, Slim 2 Iftimie, Dragoş 2 Koch, Gabriel S. 2 Majdoub, Mohamed 2 Novotný, Antonín 2 Paicu, Marius 2 Simonella, Sergio 1 Ammari, Habib M. 1 Arsénio, Diogo 1 Barilari, Davide 1 Carlen, Eric Anders 1 Dos Santos Ferreira, David 1 Fanelli, Francesco 1 Fellner, Klemens 1 Golse, François 1 Higaki, Mitsuo 1 Jabin, Pierre-Emmanuel 1 Lions, Pierre-Louis 1 Maekawa, Yasunori 1 Mullaert, Chloé 1 Nier, Francis 1 Sire, Yannick 1 Texier, Benjamin 1 Tristani, Isabelle
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### Serials

 9 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Séminaire Équations aux Dérivées Partielles 4 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 Communications in Mathematical Physics 3 Revista Matemática Iberoamericana 2 Archive for Rational Mechanics and Analysis 2 Duke Mathematical Journal 2 Mathematische Annalen 2 Mathematische Nachrichten 2 Transactions of the American Mathematical Society 2 IMRN. International Mathematics Research Notices 2 Communications in Partial Differential Equations 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 SIAM Journal on Mathematical Analysis 1 Journal d’Analyse Mathématique 1 Journal of Mathematical Analysis and Applications 1 Journal of Statistical Physics 1 Studia Mathematica 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin de la Société Mathématique de France 1 Gazette des Mathématiciens 1 Inventiones Mathematicae 1 Journal of Differential Equations 1 Journal of Functional Analysis 1 Journal of Mathematics of Kyoto University 1 Journal für die Reine und Angewandte Mathematik 1 Numerische Mathematik 1 Proceedings of the American Mathematical Society 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Differential and Integral Equations 1 Bulletin of the American Mathematical Society. New Series 1 Mémoires de la Société Mathématique de France. Nouvelle Série 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 1 Mathematical Research Letters 1 The Journal of Fourier Analysis and Applications 1 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 1 Annals of Mathematics. Second Series 1 Analysis (München) 1 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 1 Annales Henri Poincaré 1 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 1 Oberwolfach Reports 1 Astérisque 1 Oxford Lecture Series in Mathematics and its Applications 1 Discrete and Continuous Dynamical Systems. Series S 1 Analysis & PDE 1 Annals of PDE 1 Journal de l’École Polytechnique – Mathématiques 1 Zurich Lectures in Advanced Mathematics 1 Tunisian Journal of Mathematics 1 Annales Henri Lebesgue
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### Fields

 87 Partial differential equations (35-XX) 64 Fluid mechanics (76-XX) 10 Statistical mechanics, structure of matter (82-XX) 9 Geophysics (86-XX) 5 Harmonic analysis on Euclidean spaces (42-XX) 4 Abstract harmonic analysis (43-XX) 4 Probability theory and stochastic processes (60-XX) 3 Quantum theory (81-XX) 2 Topological groups, Lie groups (22-XX) 2 Real functions (26-XX) 2 Optics, electromagnetic theory (78-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Functional analysis (46-XX) 1 Operator theory (47-XX) 1 Systems theory; control (93-XX)

### Citations contained in zbMATH Open

77 Publications have been cited 1,248 times in 756 Documents Cited by Year
Mathematical geophysics. An introduction to rotating fluids and the Navier-Stokes equations. Zbl 1205.86001
Chemin, Jean-Yves; Desjardins, Benoit; Gallagher, Isabelle; Grenier, Emmanuel
2006
From Newton to Boltzmann: hard spheres and short-range potentials. Zbl 1315.82001
Gallagher, Isabelle; Saint-Raymond, Laure; Texier, Benjamin
2013
Fluids with anisotropic viscosity. Zbl 0954.76012
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel
2000
Wellposedness and stability results for the Navier-Stokes equations in $$\mathbb R^3$$. Zbl 1165.35038
Chemin, Jean-Yves; Gallagher, Isabelle
2009
Global regularity for some classes of large solutions to the Navier-Stokes equations. Zbl 1229.35168
Chemin, Jean-Yves; Gallagher, Isabelle; Paicu, Marius
2011
Asymptotics and stability for global solutions to the Navier-Stokes equations. Zbl 1038.35054
Gallagher, Isabelle; Iftimie, Dragos; Planchon, Fabrice
2003
Large, global solutions to the Navier-Stokes equations, slowly varying in one direction. Zbl 1189.35220
Chemin, Jean-Yves; Gallagher, Isabelle
2010
Anisotropy and dispersion in rotating fluids. Zbl 1034.35107
Chemin, J.-Y.; Desjardins, B.; Gallagher, I.; Grenier, E.
2002
Applications of Schochet’s methods to parabolic equations. Zbl 1101.35330
Gallagher, I.
1998
On global infinite energy solutions to the Navier-Stokes equations in two dimensions. Zbl 1027.35090
Gallagher, Isabelle; Planchon, Fabrice
2002
On the global wellposedness of the 3-D Navier–Stokes equations with large initial data. Zbl 1124.35052
Chemin, Jean-Yves; Gallagher, Isabelle
2006
The Brownian motion as the limit of a deterministic system of hard-spheres. Zbl 1337.35107
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2016
A singular limit for compressible rotating fluids. Zbl 1263.76077
Feireisl, Eduard; Gallagher, Isabelle; Novotný, Antonín
2012
Blow-up of critical Besov norms at a potential Navier-Stokes singularity. Zbl 1342.35217
Gallagher, Isabelle; Koch, Gabriel S.; Planchon, Fabrice
2016
A profile decomposition approach to the $$L^\infty _t(L^{3}_x)$$ Navier-Stokes regularity criterion. Zbl 1291.35180
Gallagher, Isabelle; Koch, Gabriel S.; Planchon, Fabrice
2013
Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity. Zbl 1096.35102
Gallagher, Isabelle; Gallay, Thierry
2005
The tridimensional Navier-Stokes equations with almost bidimensional data: Stability, uniqueness, and life span. Zbl 0893.35098
Gallagher, Isabelle
1997
Multi-scale analysis of compressible viscous and rotating fluids. Zbl 1251.35069
Feireisl, Eduard; Gallagher, Isabelle; Gerard-Varet, David; Novotný, Antonín
2012
Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator. Zbl 1180.35383
Gallagher, Isabelle; Gallay, Thierry; Nier, Francis
2009
Non-blowup at large times and stability for global solutions to the Navier-Stokes equations. (Non-explosion en temps grand et stabilité de solutions globales des équations de Navier-Stokes.) Zbl 0997.35051
Gallagher, Isabelle; Iftimie, Dragoş; Planchon, Fabrice
2002
Weak convergence results for inhomogeneous rotating fluid equations. Zbl 1132.35440
Gallagher, Isabelle; Saint-Raymond, Laure
2006
Phase-space analysis and pseudodifferential calculus on the Heisenberg group. Zbl 1246.35003
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2012
Universal dynamics for the defocusing logarithmic Schrödinger equation. Zbl 1394.35467
Carles, Rémi; Gallagher, Isabelle
2018
Ekman boundary layers in rotating fluids. Zbl 1070.35505
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel
2002
Profile decomposition for solutions of the Navier-Stokes equations. Zbl 0987.35120
Gallagher, Isabelle
2001
From hard sphere dynamics to the Stokes-Fourier equations: an $$L^2$$ analysis of the Boltzmann-Grad limit. Zbl 1403.35194
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2017
On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity. Zbl 1083.35092
Gallagher, Isabelle; Gallay, Thierry; Lions, Pierre-Louis
2005
On the stability in weak topology of the set of global solutions to the Navier-Stokes equations. Zbl 1283.35061
Bahouri, Hajer; Gallagher, Isabelle
2013
Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088
Gallagher, Isabelle; Gérard, Patrick
2001
Paraproduct on the Heisenberg group and applications. (Paraproduit sur le groupe de Heisenberg et applications.) Zbl 0971.43002
Bahouri, Hajer; Gallagher, Isabelle
2001
Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations. Zbl 1162.76016
Gallagher, Isabelle; Paicu, Marius
2009
Asymptotic of the solutions of hyperbolic equations with a skew-symmetric perturbation. Zbl 0921.35095
Gallagher, Isabelle
1998
Sums of large global solutions to the incompressible Navier-Stokes equations. Zbl 1300.35068
Chemin, Jean-Yves; Gallagher, Isabelle; Zhang, Ping
2013
Mathematical study of the betaplane model: equatorial waves and convergence results. Zbl 1151.35070
Gallagher, Isabelle; Saint-Raymond, Laure
2008
Refined Hardy inequalities. Zbl 1121.43006
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2006
Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups. Zbl 06600505
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2016
Besov algebras on Lie groups of polynomial growth. Zbl 1264.22018
Gallagher, Isabelle; Sire, Yannick
2012
On global solutions to a defocusing semi-linear wave equation. Zbl 1036.35142
Gallagher, Isabelle; Planchon, Fabrice
2003
A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations. Zbl 0997.35050
Gallagher, Isabelle
2000
Fluctuation theory in the Boltzmann-Grad limit. Zbl 1446.35089
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure; Simonella, Sergio
2020
Recent results on the incompressible limit. (Résultats récents sur la limite incompressible.) Zbl 1329.76292
Gallagher, Isabelle
2005
On pressureless gases driven by a strong inhomogeneous magnetic field. Zbl 1145.35095
Gallagher, Isabelle; Saint-Raymond, Laure
2005
From hard spheres dynamics to the Stokes-Fourier equations: an image analysis of the Boltzmann-Grad limit. (De la dynamique des sphères dures aux équations de Stokes-Fourier: une analyse $$L^2$$ de la limite de Boltzmann-Grad.) Zbl 1405.35125
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2015
The role of spectral anisotropy in the resolution of the three-dimensional Navier-Stokes equations. Zbl 1314.35080
Chemin, Jean-Yves; Gallagher, Isabelle; Mullaert, Chloé
2013
Stability estimates for an inverse scattering problem at high frequencies. Zbl 1260.35094
Ammari, Habib; Bahouri, Hajer; Dos Santos Ferreira, David; Gallagher, Isabelle
2013
One-sided convergence in the Boltzmann-Grad limit. Zbl 1416.35174
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure; Simonella, Sergio
2018
A mathematical review of the analysis of the betaplane model and equatorial waves. Zbl 1152.76055
Gallagher, Isabelle
2008
Phase-space analysis and pseudo-differential calculus on the Heisenberg group. (Analyse de l’espace des phases et calcul pseudo-differential sur le groupe de Heisenberg.) Zbl 1178.35020
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2009
Analyticity of the scattering operator for semilinear dispersive equations. Zbl 1173.35677
Carles, Rémi; Gallagher, Isabelle
2009
Asymptotics of fast rotating density-dependent incompressible fluids in two space dimensions. Zbl 1431.35123
Fanelli, Francesco; Gallagher, Isabelle
2019
Refined inequalities on graded Lie groups. Zbl 1241.22012
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2012
Precised Hardy inequalities. (Inégalités de Hardy précisées.) Zbl 1081.35169
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2005
Stability by rescaled weak convergence for the Navier-Stokes equations. (Stabilité faible pour le système de Navier-Stokes incompressible.) Zbl 1294.35056
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2014
A stability result for weak solution of the rotating fluid equation. (Un résultat de stabilité pour les solutions faibles des équations des fluides tournants.) Zbl 0878.76081
Gallagher, Isabelle
1997
The heat kernel and frequency localized functions on the Heisenberg group. Zbl 1202.43005
Bahouri, Hajer; Gallagher, Isabelle
2009
On the role of quadratic oscillations in nonlinear Schrödinger equations. Zbl 1059.35134
Carles, Rémi; Fermanian Kammerer, Clotilde; Gallagher, Isabelle
2003
Existence and uniqueness of solutions for the axisymmetric Navier-Stokes system. (Existence et unicité de solutions pour le système de Navier-Stokes axisymétrique.) Zbl 0998.35035
Gallagher, Isabelle; Ibrahim, Slim; Majdoub, Mohamed
2001
From Newton to Navier-Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales. Zbl 1420.35186
Gallagher, Isabelle
2019
Semiclassical and spectral analysis of oceanic waves. Zbl 1244.35147
Cheverry, Christophe; Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure
2012
On the convergence of smooth solutions from Boltzmann to Navier-Stokes. (Sur la convergence de solutions régulières de Boltzmann vers Navier-Stokes.) Zbl 1448.35393
Gallagher, Isabelle; Tristani, Isabelle
2020
Trapping Rossby waves. Zbl 1177.35162
Cheverry, Christophe; Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure
2009
A nonlinear estimate of the life span of solutions of the three dimensional Navier-Stokes equations. Zbl 1407.76027
Chemin, Jean-Yves; Gallagher, Isabelle
2019
Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations. Zbl 1161.76456
Gallagher, Isabelle
2003
On stationary two-dimensional flows around a fast rotating disk. Zbl 1414.35148
Gallagher, Isabelle; Higaki, Mitsuo; Maekawa, Yasunori
2019
On the radius of analyticity of solutions to semi-linear parabolic systems. Zbl 1459.35234
Chemin, Jean-Yves; Gallagher, Isabelle; Zhang, Ping
2020
Anisotropy and dispersion in rotating fluids. (Anisotropie et dispersion dans les fluides tournants.) Zbl 0961.76085
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel
1999
Global existence for geostrophic fluid equations. (Existence globale pour des équations des fluides géostrophiques.) Zbl 0992.76094
Gallagher, Isabelle
1997
On the propagation of oceanic waves driven by a strong macroscopic flow. Zbl 1252.35266
Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure
2012
Some stability results on global solutions to the Navier-Stokes equations. Zbl 1321.35135
Gallagher, Isabelle
2015
Some remarks about the possible blow-up for the Navier-Stokes equations. Zbl 1428.35277
Chemin, Jean-Yves; Gallagher, Isabelle; Zhang, Ping
2019
Weak convergence results for inhomogeneous rotating fluid equations. Zbl 1044.76067
Gallagher, Isabelle; Saint-Raymond, Laure
2003
Strichartz estimates and Fourier restriction theorems on the Heisenberg group. Zbl 1460.35365
Bahouri, Hajer; Barilari, Davide; Gallagher, Isabelle
2021
Precised Hardy inequalities on $$\mathbb R^{ d }$$ and on the Heisenberg group $$H^{ d }$$. Zbl 1292.46020
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2005
Profile decomposition of solutions of the Navier-Stokes equations. (Décomposition en profils des solutions des équations de Navier-Stokes.) Zbl 1067.35062
Gallagher, Isabelle
2000
Remarks on the global regularity for solutions to the incompressible Navier-Stokes equations. Zbl 1364.35238
Gallagher, Isabelle
2013
Derivation of an Ornstein-Uhlenbeck process for a massive particle in a rarified gas of particles. Zbl 1436.82020
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2018
Solutions of Navier-Stokes-Maxwell systems in large energy spaces. Zbl 1440.35261
Arsénio, Diogo; Gallagher, Isabelle
2020
Strichartz estimates and Fourier restriction theorems on the Heisenberg group. Zbl 1460.35365
Bahouri, Hajer; Barilari, Davide; Gallagher, Isabelle
2021
Fluctuation theory in the Boltzmann-Grad limit. Zbl 1446.35089
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure; Simonella, Sergio
2020
On the convergence of smooth solutions from Boltzmann to Navier-Stokes. (Sur la convergence de solutions régulières de Boltzmann vers Navier-Stokes.) Zbl 1448.35393
Gallagher, Isabelle; Tristani, Isabelle
2020
On the radius of analyticity of solutions to semi-linear parabolic systems. Zbl 1459.35234
Chemin, Jean-Yves; Gallagher, Isabelle; Zhang, Ping
2020
Solutions of Navier-Stokes-Maxwell systems in large energy spaces. Zbl 1440.35261
Arsénio, Diogo; Gallagher, Isabelle
2020
Asymptotics of fast rotating density-dependent incompressible fluids in two space dimensions. Zbl 1431.35123
Fanelli, Francesco; Gallagher, Isabelle
2019
From Newton to Navier-Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales. Zbl 1420.35186
Gallagher, Isabelle
2019
A nonlinear estimate of the life span of solutions of the three dimensional Navier-Stokes equations. Zbl 1407.76027
Chemin, Jean-Yves; Gallagher, Isabelle
2019
On stationary two-dimensional flows around a fast rotating disk. Zbl 1414.35148
Gallagher, Isabelle; Higaki, Mitsuo; Maekawa, Yasunori
2019
Some remarks about the possible blow-up for the Navier-Stokes equations. Zbl 1428.35277
Chemin, Jean-Yves; Gallagher, Isabelle; Zhang, Ping
2019
Universal dynamics for the defocusing logarithmic Schrödinger equation. Zbl 1394.35467
Carles, Rémi; Gallagher, Isabelle
2018
One-sided convergence in the Boltzmann-Grad limit. Zbl 1416.35174
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure; Simonella, Sergio
2018
Derivation of an Ornstein-Uhlenbeck process for a massive particle in a rarified gas of particles. Zbl 1436.82020
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2018
From hard sphere dynamics to the Stokes-Fourier equations: an $$L^2$$ analysis of the Boltzmann-Grad limit. Zbl 1403.35194
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2017
The Brownian motion as the limit of a deterministic system of hard-spheres. Zbl 1337.35107
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2016
Blow-up of critical Besov norms at a potential Navier-Stokes singularity. Zbl 1342.35217
Gallagher, Isabelle; Koch, Gabriel S.; Planchon, Fabrice
2016
Dispersive estimates for the Schrödinger operator on step-2 stratified Lie groups. Zbl 06600505
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2016
From hard spheres dynamics to the Stokes-Fourier equations: an image analysis of the Boltzmann-Grad limit. (De la dynamique des sphères dures aux équations de Stokes-Fourier: une analyse $$L^2$$ de la limite de Boltzmann-Grad.) Zbl 1405.35125
Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure
2015
Some stability results on global solutions to the Navier-Stokes equations. Zbl 1321.35135
Gallagher, Isabelle
2015
Stability by rescaled weak convergence for the Navier-Stokes equations. (Stabilité faible pour le système de Navier-Stokes incompressible.) Zbl 1294.35056
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2014
From Newton to Boltzmann: hard spheres and short-range potentials. Zbl 1315.82001
Gallagher, Isabelle; Saint-Raymond, Laure; Texier, Benjamin
2013
A profile decomposition approach to the $$L^\infty _t(L^{3}_x)$$ Navier-Stokes regularity criterion. Zbl 1291.35180
Gallagher, Isabelle; Koch, Gabriel S.; Planchon, Fabrice
2013
On the stability in weak topology of the set of global solutions to the Navier-Stokes equations. Zbl 1283.35061
Bahouri, Hajer; Gallagher, Isabelle
2013
Sums of large global solutions to the incompressible Navier-Stokes equations. Zbl 1300.35068
Chemin, Jean-Yves; Gallagher, Isabelle; Zhang, Ping
2013
The role of spectral anisotropy in the resolution of the three-dimensional Navier-Stokes equations. Zbl 1314.35080
Chemin, Jean-Yves; Gallagher, Isabelle; Mullaert, Chloé
2013
Stability estimates for an inverse scattering problem at high frequencies. Zbl 1260.35094
Ammari, Habib; Bahouri, Hajer; Dos Santos Ferreira, David; Gallagher, Isabelle
2013
Remarks on the global regularity for solutions to the incompressible Navier-Stokes equations. Zbl 1364.35238
Gallagher, Isabelle
2013
A singular limit for compressible rotating fluids. Zbl 1263.76077
Feireisl, Eduard; Gallagher, Isabelle; Novotný, Antonín
2012
Multi-scale analysis of compressible viscous and rotating fluids. Zbl 1251.35069
Feireisl, Eduard; Gallagher, Isabelle; Gerard-Varet, David; Novotný, Antonín
2012
Phase-space analysis and pseudodifferential calculus on the Heisenberg group. Zbl 1246.35003
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2012
Besov algebras on Lie groups of polynomial growth. Zbl 1264.22018
Gallagher, Isabelle; Sire, Yannick
2012
Refined inequalities on graded Lie groups. Zbl 1241.22012
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2012
Semiclassical and spectral analysis of oceanic waves. Zbl 1244.35147
Cheverry, Christophe; Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure
2012
On the propagation of oceanic waves driven by a strong macroscopic flow. Zbl 1252.35266
Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure
2012
Global regularity for some classes of large solutions to the Navier-Stokes equations. Zbl 1229.35168
Chemin, Jean-Yves; Gallagher, Isabelle; Paicu, Marius
2011
Large, global solutions to the Navier-Stokes equations, slowly varying in one direction. Zbl 1189.35220
Chemin, Jean-Yves; Gallagher, Isabelle
2010
Wellposedness and stability results for the Navier-Stokes equations in $$\mathbb R^3$$. Zbl 1165.35038
Chemin, Jean-Yves; Gallagher, Isabelle
2009
Spectral asymptotics for large skew-symmetric perturbations of the harmonic oscillator. Zbl 1180.35383
Gallagher, Isabelle; Gallay, Thierry; Nier, Francis
2009
Remarks on the blow-up of solutions to a toy model for the Navier-Stokes equations. Zbl 1162.76016
Gallagher, Isabelle; Paicu, Marius
2009
Phase-space analysis and pseudo-differential calculus on the Heisenberg group. (Analyse de l’espace des phases et calcul pseudo-differential sur le groupe de Heisenberg.) Zbl 1178.35020
Bahouri, Hajer; Fermanian-Kammerer, Clotilde; Gallagher, Isabelle
2009
Analyticity of the scattering operator for semilinear dispersive equations. Zbl 1173.35677
Carles, Rémi; Gallagher, Isabelle
2009
The heat kernel and frequency localized functions on the Heisenberg group. Zbl 1202.43005
Bahouri, Hajer; Gallagher, Isabelle
2009
Trapping Rossby waves. Zbl 1177.35162
Cheverry, Christophe; Gallagher, Isabelle; Paul, Thierry; Saint-Raymond, Laure
2009
Mathematical study of the betaplane model: equatorial waves and convergence results. Zbl 1151.35070
Gallagher, Isabelle; Saint-Raymond, Laure
2008
A mathematical review of the analysis of the betaplane model and equatorial waves. Zbl 1152.76055
Gallagher, Isabelle
2008
Mathematical geophysics. An introduction to rotating fluids and the Navier-Stokes equations. Zbl 1205.86001
Chemin, Jean-Yves; Desjardins, Benoit; Gallagher, Isabelle; Grenier, Emmanuel
2006
On the global wellposedness of the 3-D Navier–Stokes equations with large initial data. Zbl 1124.35052
Chemin, Jean-Yves; Gallagher, Isabelle
2006
Weak convergence results for inhomogeneous rotating fluid equations. Zbl 1132.35440
Gallagher, Isabelle; Saint-Raymond, Laure
2006
Refined Hardy inequalities. Zbl 1121.43006
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2006
Uniqueness for the two-dimensional Navier-Stokes equation with a measure as initial vorticity. Zbl 1096.35102
Gallagher, Isabelle; Gallay, Thierry
2005
On the uniqueness of the solution of the two-dimensional Navier–Stokes equation with a Dirac mass as initial vorticity. Zbl 1083.35092
Gallagher, Isabelle; Gallay, Thierry; Lions, Pierre-Louis
2005
Recent results on the incompressible limit. (Résultats récents sur la limite incompressible.) Zbl 1329.76292
Gallagher, Isabelle
2005
On pressureless gases driven by a strong inhomogeneous magnetic field. Zbl 1145.35095
Gallagher, Isabelle; Saint-Raymond, Laure
2005
Precised Hardy inequalities. (Inégalités de Hardy précisées.) Zbl 1081.35169
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2005
Precised Hardy inequalities on $$\mathbb R^{ d }$$ and on the Heisenberg group $$H^{ d }$$. Zbl 1292.46020
Bahouri, Hajer; Chemin, Jean-Yves; Gallagher, Isabelle
2005
Asymptotics and stability for global solutions to the Navier-Stokes equations. Zbl 1038.35054
Gallagher, Isabelle; Iftimie, Dragos; Planchon, Fabrice
2003
On global solutions to a defocusing semi-linear wave equation. Zbl 1036.35142
Gallagher, Isabelle; Planchon, Fabrice
2003
On the role of quadratic oscillations in nonlinear Schrödinger equations. Zbl 1059.35134
Carles, Rémi; Fermanian Kammerer, Clotilde; Gallagher, Isabelle
2003
Stability and weak-strong uniqueness for axisymmetric solutions of the Navier-Stokes equations. Zbl 1161.76456
Gallagher, Isabelle
2003
Weak convergence results for inhomogeneous rotating fluid equations. Zbl 1044.76067
Gallagher, Isabelle; Saint-Raymond, Laure
2003
Anisotropy and dispersion in rotating fluids. Zbl 1034.35107
Chemin, J.-Y.; Desjardins, B.; Gallagher, I.; Grenier, E.
2002
On global infinite energy solutions to the Navier-Stokes equations in two dimensions. Zbl 1027.35090
Gallagher, Isabelle; Planchon, Fabrice
2002
Non-blowup at large times and stability for global solutions to the Navier-Stokes equations. (Non-explosion en temps grand et stabilité de solutions globales des équations de Navier-Stokes.) Zbl 0997.35051
Gallagher, Isabelle; Iftimie, Dragoş; Planchon, Fabrice
2002
Ekman boundary layers in rotating fluids. Zbl 1070.35505
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel
2002
Profile decomposition for solutions of the Navier-Stokes equations. Zbl 0987.35120
Gallagher, Isabelle
2001
Profile decomposition for the wave equation outside a convex obstacle. Zbl 0980.35088
Gallagher, Isabelle; Gérard, Patrick
2001
Paraproduct on the Heisenberg group and applications. (Paraproduit sur le groupe de Heisenberg et applications.) Zbl 0971.43002
Bahouri, Hajer; Gallagher, Isabelle
2001
Existence and uniqueness of solutions for the axisymmetric Navier-Stokes system. (Existence et unicité de solutions pour le système de Navier-Stokes axisymétrique.) Zbl 0998.35035
Gallagher, Isabelle; Ibrahim, Slim; Majdoub, Mohamed
2001
Fluids with anisotropic viscosity. Zbl 0954.76012
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel
2000
A remark on smooth solutions of the weakly compressible periodic Navier-Stokes equations. Zbl 0997.35050
Gallagher, Isabelle
2000
Profile decomposition of solutions of the Navier-Stokes equations. (Décomposition en profils des solutions des équations de Navier-Stokes.) Zbl 1067.35062
Gallagher, Isabelle
2000
Anisotropy and dispersion in rotating fluids. (Anisotropie et dispersion dans les fluides tournants.) Zbl 0961.76085
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel
1999
Applications of Schochet’s methods to parabolic equations. Zbl 1101.35330
Gallagher, I.
1998
Asymptotic of the solutions of hyperbolic equations with a skew-symmetric perturbation. Zbl 0921.35095
Gallagher, Isabelle
1998
The tridimensional Navier-Stokes equations with almost bidimensional data: Stability, uniqueness, and life span. Zbl 0893.35098
Gallagher, Isabelle
1997
A stability result for weak solution of the rotating fluid equation. (Un résultat de stabilité pour les solutions faibles des équations des fluides tournants.) Zbl 0878.76081
Gallagher, Isabelle
1997
Global existence for geostrophic fluid equations. (Existence globale pour des équations des fluides géostrophiques.) Zbl 0992.76094
Gallagher, Isabelle
1997
all top 5

### Cited by 768 Authors

 43 Gallagher, Isabelle 24 Zhang, Ping 22 Chemin, Jean-Yves 18 Paicu, Marius 17 Bahouri, Hajer 16 Saint-Raymond, Laure 13 Zhang, Zhifei 12 Carles, Rémi 10 Bedrossian, Jacob 10 Fermanian-Kammerer, Clotilde 9 Fanelli, Francesco 9 Masmoudi, Nader 9 Zhang, Ting 8 Barker, Tobias 8 Briant, Marc 8 Nota, Alessia 8 Pulvirenti, Mario 8 Wu, Gang 7 Charve, Frédéric 7 Cheverry, Christophe 7 Fang, Daoyuan 7 Feireisl, Eduard 7 Gérard-Varet, David 7 Germain, Pierre 7 Novotný, Antonín 7 Schochet, Steven H. 7 Scrobogna, Stefano 7 Simonella, Sergio 7 Zhai, Xiaoping 6 Bodineau, Thierry 6 Fischer, Véronique 6 Gallay, Thierry 6 Li, Yongsheng 6 Nečasová, Šárka 6 Robinson, James Cooper 6 Ruzhansky, Michael V. 6 Takada, Ryo 6 Zheng, Xiaoxin 5 Bernicot, Frédéric 5 Danchin, Raphaël 5 Górka, Przemysław 5 Gui, Guilong 5 Ju, Qiangchang 5 Li, Fucai 5 Maekawa, Yasunori 5 Miao, Changxing 5 Ngo, Van-Sang 5 Planchon, Fabrice 5 Velázquez, Juan J. L. 5 Yoneda, Tsuyoshi 5 Zajączkowski, Wojciech M. 4 Abidi, Hammadi 4 Albritton, Dallas 4 Benameur, Jamel 4 Chen, Qionglei 4 Coti Zelati, Michele 4 Denlinger, Ryan 4 Ferreira, Lucas Catão de Freitas 4 Frey, Dorothee 4 Haspot, Boris 4 Houamed, Haroune 4 Ibrahim, Slim 4 Iftimie, Dragoş 4 Jiang, Song 4 Kostrzewa, Tomasz 4 Kukavica, Igor 4 Kwon, Young-Sam 4 Lin, Fang Hua 4 Liu, Yanlin 4 Majdoub, Mohamed 4 McCormick, David S. 4 Peloso, Marco Maria 4 Rodrigo, José Luis 4 Rusin, Walter M. 4 Selmi, Ridha 4 Su, Chunmei 4 Sun, Jinyi 4 Šverák, Vladimír 4 Temam, Roger Meyer 4 Titi, Edriss Saleh 4 Vallarino, Maria 4 Wu, Jiahong 4 Ziane, Mohammed 3 Bao, Weizhu 3 Bchatnia, Ahmed 3 Bessaih, Hakima 3 Bouchet, Freddy 3 Bruno, Tommaso 3 Carrapatoso, Kleber 3 De Anna, Francesco 3 Degond, Pierre 3 Dutrifoy, Alexandre 3 Duyckaerts, Thomas 3 Ferriere, Guillaume 3 Frank, Rupert L. 3 Giga, Yoshikazu 3 Grenier, Emmanuel 3 Han-Kwan, Daniel 3 Hani, Zaher 3 Iwabuchi, Tsukasa ...and 668 more Authors
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### Cited in 163 Serials

 48 Archive for Rational Mechanics and Analysis 46 Journal of Differential Equations 28 Communications in Mathematical Physics 28 Journal of Mathematical Analysis and Applications 28 Journal of Mathematical Fluid Mechanics 26 Discrete and Continuous Dynamical Systems 21 Journal of Functional Analysis 20 Journal de Mathématiques Pures et Appliquées. Neuvième Série 17 Journal of Statistical Physics 17 Comptes Rendus. Mathématique. Académie des Sciences, Paris 16 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 16 Communications in Partial Differential Equations 15 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 14 ZAMP. Zeitschrift für angewandte Mathematik und Physik 14 Advances in Mathematics 12 Physica D 12 Nonlinear Analysis. Real World Applications 11 Nonlinearity 11 SIAM Journal on Mathematical Analysis 11 Kinetic and Related Models 10 Communications on Pure and Applied Mathematics 10 Journal of Mathematical Physics 10 Mathematische Annalen 10 Revista Matemática Iberoamericana 10 Journal of Evolution Equations 8 Applied Mathematics Letters 8 Journal of Nonlinear Science 6 Mathematical Methods in the Applied Sciences 6 Transactions of the American Mathematical Society 6 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 6 Science China. Mathematics 5 Computers & Mathematics with Applications 5 Journal d’Analyse Mathématique 5 Annales de l’Institut Fourier 5 Inventiones Mathematicae 5 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 5 Journal of the Institute of Mathematics of Jussieu 5 Annals of PDE 4 Annali di Matematica Pura ed Applicata. Serie Quarta 4 Numerische Mathematik 4 Acta Applicandae Mathematicae 4 Bulletin of the American Mathematical Society. New Series 4 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 4 The Journal of Fourier Analysis and Applications 4 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 4 Communications on Pure and Applied Analysis 4 Annali della Scuola Normale Superiore di Pisa. Classe di Scienze. Serie V 3 Applicable Analysis 3 Applied Mathematics and Optimization 3 Memoirs of the American Mathematical Society 3 Proceedings of the American Mathematical Society 3 Asymptotic Analysis 3 The Journal of Geometric Analysis 3 Journal of Dynamics and Differential Equations 3 Calculus of Variations and Partial Differential Equations 3 M2AN. Mathematical Modelling and Numerical Analysis. ESAIM, European Series in Applied and Industrial Mathematics 3 Communications in Contemporary Mathematics 3 Acta Mathematica Scientia. Series B. (English Edition) 3 Journal de l’École Polytechnique – Mathématiques 3 Séminaire Laurent Schwartz. EDP et Applications 3 Annales Henri Lebesgue 3 SN Partial Differential Equations and Applications 2 Journal of Computational Physics 2 Bulletin de la Société Mathématique de France 2 Duke Mathematical Journal 2 International Journal of Mathematics and Mathematical Sciences 2 Mathematische Zeitschrift 2 Monatshefte für Mathematik 2 Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Serie IX. Rendiconti Lincei. Matematica e Applicazioni 2 Stochastic Processes and their Applications 2 Applied Mathematics. Series B (English Edition) 2 Journal of Mathematical Sciences (New York) 2 Bulletin des Sciences Mathématiques 2 Annales Academiae Scientiarum Fennicae. Mathematica 2 Journal of Inequalities and Applications 2 Annals of Mathematics. Second Series 2 Journal of the European Mathematical Society (JEMS) 2 Acta Mathematica Sinica. English Series 2 Annales Henri Poincaré 2 Mathematical Modelling and Analysis 2 Discrete and Continuous Dynamical Systems. Series B 2 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 2 Analysis and Applications (Singapore) 2 Annali dell’Università di Ferrara. Sezione VII. Scienze Matematiche 2 Discrete and Continuous Dynamical Systems. Series S 2 Analysis & PDE 2 Journal of Applied Analysis and Computation 2 Journal of Elliptic and Parabolic Equations 2 Tunisian Journal of Mathematics 1 Acta Mechanica 1 Computer Methods in Applied Mechanics and Engineering 1 Physics Letters. A 1 Arkiv för Matematik 1 Mathematics of Computation 1 Reviews in Mathematical Physics 1 The Annals of Probability 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Archiv der Mathematik 1 Colloquium Mathematicum 1 Publications Mathématiques ...and 63 more Serials
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### Cited in 43 Fields

 673 Partial differential equations (35-XX) 475 Fluid mechanics (76-XX) 84 Statistical mechanics, structure of matter (82-XX) 49 Harmonic analysis on Euclidean spaces (42-XX) 42 Probability theory and stochastic processes (60-XX) 40 Functional analysis (46-XX) 37 Geophysics (86-XX) 26 Quantum theory (81-XX) 23 Dynamical systems and ergodic theory (37-XX) 23 Operator theory (47-XX) 22 Topological groups, Lie groups (22-XX) 22 Abstract harmonic analysis (43-XX) 16 Numerical analysis (65-XX) 12 Global analysis, analysis on manifolds (58-XX) 10 Real functions (26-XX) 9 Mechanics of particles and systems (70-XX) 9 Classical thermodynamics, heat transfer (80-XX) 9 Biology and other natural sciences (92-XX) 8 Functions of a complex variable (30-XX) 8 Systems theory; control (93-XX) 7 Ordinary differential equations (34-XX) 7 Calculus of variations and optimal control; optimization (49-XX) 6 Mechanics of deformable solids (74-XX) 6 Optics, electromagnetic theory (78-XX) 5 Differential geometry (53-XX) 4 Integral equations (45-XX) 3 Integral transforms, operational calculus (44-XX) 2 Nonassociative rings and algebras (17-XX) 2 Measure and integration (28-XX) 2 Approximations and expansions (41-XX) 2 General topology (54-XX) 2 Information and communication theory, circuits (94-XX) 1 General and overarching topics; collections (00-XX) 1 History and biography (01-XX) 1 Mathematical logic and foundations (03-XX) 1 Combinatorics (05-XX) 1 Algebraic geometry (14-XX) 1 Potential theory (31-XX) 1 Computer science (68-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Operations research, mathematical programming (90-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX)

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