ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN)

Stability to the Incompressible Navier-Stokes Equations

Guilong Gui
Springer Theses, Stability to the Incompressible Navier-Stokes Equations 1 (2013)
DOI: 10.1007/978-3-642-36028-2_1
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Stability to the Incompressible Navier-Stokes Equations

Guilong Gui
Springer Theses, Stability to the Incompressible Navier-Stokes Equations 25 (2013)
DOI: 10.1007/978-3-642-36028-2_2
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Asymptotics and Lower Bound for the Lifespan of Solutions to the Primitive Equations

Frédéric Charve
Acta Applicandae Mathematicae 158 (1) 11 (2018)
DOI: 10.1007/s10440-018-0172-3
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Advanced Computational Methods for Knowledge Engineering

Van-Sang Ngo
Studies in Computational Intelligence, Advanced Computational Methods for Knowledge Engineering 479 187 (2013)
DOI: 10.1007/978-3-319-00293-4_15
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Advances in Mathematical Fluid Mechanics

Luigi C. Berselli and Franco Flandoli
Advances in Mathematical Fluid Mechanics 55 (2009)
DOI: 10.1007/978-3-642-04068-9_5
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Ekman boundary layers in rotating fluids

Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher and Emmanuel Grenier
ESAIM: Control, Optimisation and Calculus of Variations 8 441 (2002)
DOI: 10.1051/cocv:2002037
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Rotating Fluids with Small Viscosity

V.-S. Ngo
International Mathematics Research Notices (2009)
DOI: 10.1093/imrn/rnp004
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Derivation of limit equations for a singular perturbation of a 3D periodic Boussinesq system

Stefano Scrobogna
Discrete and Continuous Dynamical Systems 37 (12) 5979 (2017)
DOI: 10.3934/dcds.2017259
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Dispersive effects of weakly compressible and fast rotating inviscid fluids

Stefano Scrobogna and Van-Sang Ngo
Discrete and Continuous Dynamical Systems 38 (2) 749 (2017)
DOI: 10.3934/dcds.2018033
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On Two-Dimensional Magnetic Bénard Problem with Mixed Partial Viscosity

Jianfeng Cheng and Lili Du
Journal of Mathematical Fluid Mechanics 17 (4) 769 (2015)
DOI: 10.1007/s00021-015-0224-7
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A Global Existence Result for the Anisotropic Rotating Magnetohydrodynamical Systems

Van-Sang Ngo
Acta Applicandae Mathematicae 150 (1) 1 (2017)
DOI: 10.1007/s10440-016-0092-z
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Horizontal Large Eddy Simulation of Stratified Mixing in a Lock-Exchange System

Luigi C. Berselli, Paul F. Fischer, Traian Iliescu and Tamay M. Özgökmen
Journal of Scientific Computing 49 (1) 3 (2011)
DOI: 10.1007/s10915-011-9464-8
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On the Global Well-posedness for the Boussinesq System with Horizontal Dissipation

Changxing Miao and Xiaoxin Zheng
Communications in Mathematical Physics 321 (1) 33 (2013)
DOI: 10.1007/s00220-013-1721-2
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Examples of dispersive effects in non-viscous rotating fluids

Alexandre Dutrifoy
Journal de Mathématiques Pures et Appliquées 84 (3) 331 (2005)
DOI: 10.1016/j.matpur.2004.09.007
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On the Global Wellposedness to the 3-D Incompressible Anisotropic Navier-Stokes Equations

Jean-Yves Chemin and Ping Zhang
Communications in Mathematical Physics 272 (2) 529 (2007)
DOI: 10.1007/s00220-007-0236-0
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Analysis of a Large Eddy Simulation model based on anisotropic filtering

Luigi C. Berselli
Journal of Mathematical Analysis and Applications 386 (1) 149 (2012)
DOI: 10.1016/j.jmaa.2011.07.044
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On the global well-posedness to the 3-D incompressible anisotropic magnetohydrodynamics equations

Gaocheng Yue and Chengkui Zhong
Discrete and Continuous Dynamical Systems 36 (10) 5801 (2016)
DOI: 10.3934/dcds.2016055
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Global regularity for some classes of large solutions to the Navier-Stokes equations

Jean-Yves Chemin, Isabelle Gallagher and Marius Paicu
Annals of Mathematics 173 (2) 983 (2011)
DOI: 10.4007/annals.2011.173.2.9
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Global Small Solutions to Three-Dimensional Incompressible Magnetohydrodynamical System

Li Xu and Ping Zhang
SIAM Journal on Mathematical Analysis 47 (1) 26 (2015)
DOI: 10.1137/14095515X
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Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov–Sobolev-type spaces

Haitao Ma, Xiaoping Zhai, Wei Yan and Yongsheng Li
Zeitschrift für angewandte Mathematik und Physik 68 (1) (2017)
DOI: 10.1007/s00033-016-0761-9
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A Uniqueness Result for the Navier--Stokes Equations with Vanishing Vertical Viscosity

Dragos Iftimie
SIAM Journal on Mathematical Analysis 33 (6) 1483 (2002)
DOI: 10.1137/S0036141000382126
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Équation Périodique de Navier–Stokes sans Viscosité dans une Direction

Marius Paicu
Communications in Partial Differential Equations 30 (8) 1107 (2005)
DOI: 10.1080/036053005002575529
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Global Wellposed Problem for the 3-D Incompressible Anisotropic Navier-Stokes Equations in an Anisotropic Space

Ting Zhang
Communications in Mathematical Physics 287 (1) 211 (2009)
DOI: 10.1007/s00220-008-0631-1
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Global well-posedness for the 3D rotating Navier–Stokes equations with highly oscillating initial data

Qionglei Chen, Changxing Miao and Zhifei Zhang
Pacific Journal of Mathematics 262 (2) 263 (2013)
DOI: 10.2140/pjm.2013.262.263
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On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data

Marius Paicu and Ping Zhang
Annales de l'Institut Henri Poincare (C) Non Linear Analysis 32 (4) 813 (2015)
DOI: 10.1016/j.anihpc.2014.03.006
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Global Small Solutions to an MHD-Type System: The Three-Dimensional Case

Fanghua Lin and Ping Zhang
Communications on Pure and Applied Mathematics 67 (4) 531 (2014)
DOI: 10.1002/cpa.21506
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On the regularity criteria of the 2D Boussinesq equations with partial dissipation

Zhuan Ye
Computers & Mathematics with Applications 72 (7) 1880 (2016)
DOI: 10.1016/j.camwa.2016.08.007
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A deterministic model for the propagation of turbulent oscillations

C. Cheverry
Journal of Differential Equations 247 (9) 2637 (2009)
DOI: 10.1016/j.jde.2009.08.009
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Global regularity for the Navier–Stokes equations with some classes of large initial data

Marius Paicu and Zhifei Zhang
Analysis & PDE 4 (1) 95 (2011)
DOI: 10.2140/apde.2011.4.95
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Wellposedness for anisotropic rotating fluid equations

Dao-yuan Fang, Su-mei Wang and Ting Zhang
Applied Mathematics-A Journal of Chinese Universities 27 (1) 9 (2012)
DOI: 10.1007/s11766-012-2534-3
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Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions

Dragoş Iftimie and Gabriela Planas
Nonlinearity 19 (4) 899 (2006)
DOI: 10.1088/0951-7715/19/4/007
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Global regularity for the 3D axisymmetric MHD Equations with horizontal dissipation and vertical magnetic diffusion

Jitao Liu and Quansen Jiu
Discrete and Continuous Dynamical Systems 35 (1) 301 (2014)
DOI: 10.3934/dcds.2015.35.301
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Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data

Marius Paicu and Zhifei Zhang
Journal of the Institute of Mathematics of Jussieu 13 (2) 395 (2014)
DOI: 10.1017/S1474748013000212
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The inviscid limit of the incompressible anisotropic Navier–Stokes equations with the non-slip boundary condition

Cheng-Jie Liu and Ya-Guang Wang
Zeitschrift für angewandte Mathematik und Physik 64 (4) 1187 (2013)
DOI: 10.1007/s00033-012-0281-1
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A solution to parabolic system with the fractional Laplacian

Lin Fang and Dao-yuan Fang
Applied Mathematics-A Journal of Chinese Universities 24 (2) 184 (2009)
DOI: 10.1007/s11766-009-2084-5
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Étude asymptotique pour les fluides anisotropes en rotation rapide dans le cas périodique

Marius Paicu
Journal de Mathématiques Pures et Appliquées 83 (2) 163 (2004)
DOI: 10.1016/j.matpur.2003.10.001
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Global wellposed problem for the 3-D incompressible anisotropic Navier–Stokes equations

Ting Zhang and Daoyuan Fang
Journal de Mathématiques Pures et Appliquées 90 (5) 413 (2008)
DOI: 10.1016/j.matpur.2008.06.008
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Stability to the global large solutions of 3-D Navier–Stokes equations

Guilong Gui and Ping Zhang
Advances in Mathematics 225 (3) 1248 (2010)
DOI: 10.1016/j.aim.2010.03.022
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Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

H. B. de Oliveira
Analysis and Applications 17 (06) 977 (2019)
DOI: 10.1142/S021953051950009X
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GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

RAPHAËL DANCHIN and MARIUS PAICU
Mathematical Models and Methods in Applied Sciences 21 (03) 421 (2011)
DOI: 10.1142/S0218202511005106
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On 3D Navier–Stokes equations: Regularization and uniqueness by delays

Hakima Bessaih, María J. Garrido-Atienza and Björn Schmalfuß
Physica D: Nonlinear Phenomena 376-377 228 (2018)
DOI: 10.1016/j.physd.2018.03.004
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Global large solutions to 3-D inhomogeneous Navier–Stokes system with one slow variable

Jean-Yves Chemin, Marius Paicu and Ping Zhang
Journal of Differential Equations 256 (1) 223 (2014)
DOI: 10.1016/j.jde.2013.09.004
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On stochastic modified 3D Navier–Stokes equations with anisotropic viscosity

Hakima Bessaih and Annie Millet
Journal of Mathematical Analysis and Applications 462 (1) 915 (2018)
DOI: 10.1016/j.jmaa.2017.12.053
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Evolution problems of Navier–Stokes type with anisotropic diffusion

S. N. Antontsev and H. B. de Oliveira
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 110 (2) 729 (2016)
DOI: 10.1007/s13398-015-0262-2
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A priori estimates for the 3D quasi-geostrophic system

Frédéric Charve
Journal of Mathematical Analysis and Applications 444 (2) 911 (2016)
DOI: 10.1016/j.jmaa.2016.06.056
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Convergence results for MHD system

Ridha Selmi
International Journal of Mathematics and Mathematical Sciences 2006 1 (2006)
DOI: 10.1155/IJMMS/2006/28704
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Anisotropic Regularity Conditions for the Suitable Weak Solutions to the 3D Navier–Stokes Equations

Yanqing Wang and Gang Wu
Journal of Mathematical Fluid Mechanics 18 (4) 699 (2016)
DOI: 10.1007/s00021-016-0279-0
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Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations

Hakima Bessaih, Saber Trabelsi and Hamdi Zorgati
ESAIM: Mathematical Modelling and Numerical Analysis 50 (6) 1817 (2016)
DOI: 10.1051/m2an/2016008
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THE VLASOV–POISSON SYSTEM WITH STRONG MAGNETIC FIELD IN QUASINEUTRAL REGIME

F. GOLSE and L. SAINT-RAYMOND
Mathematical Models and Methods in Applied Sciences 13 (05) 661 (2003)
DOI: 10.1142/S0218202503002647
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Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion

Xiaoxia Ren, Jiahong Wu, Zhaoyin Xiang and Zhifei Zhang
Journal of Functional Analysis 267 (2) 503 (2014)
DOI: 10.1016/j.jfa.2014.04.020
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Global well-posedness of the three dimensional incompressible anisotropic Navier–Stokes system

Kai Yan and Zhaoyang Yin
Nonlinear Analysis: Real World Applications 32 52 (2016)
DOI: 10.1016/j.nonrwa.2016.03.015
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Global regularity for generalized anisotropic Navier–Stokes equations

Ting Zhang
Journal of Mathematical Physics 51 (12) 123503 (2010)
DOI: 10.1063/1.3519382
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On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics with horizontal dissipation

Minggang Fei and Zhaoyin Xiang
Journal of Mathematical Physics 56 (5) 051504 (2015)
DOI: 10.1063/1.4921653
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Global small solutions of 2-D incompressible MHD system

Fanghua Lin, Li Xu and Ping Zhang
Journal of Differential Equations 259 (10) 5440 (2015)
DOI: 10.1016/j.jde.2015.06.034
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Some remarks about the possible blow-up for the Navier-Stokes equations

Jean-Yves Chemin, Isabelle Gallagher and Ping Zhang
Communications in Partial Differential Equations 44 (12) 1387 (2019)
DOI: 10.1080/03605302.2019.1641725
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Vanishing vertical viscosity limit of anisotropic Navier–Stokes equation with no-slip boundary condition

Tao Tao
Journal of Differential Equations 265 (9) 4283 (2018)
DOI: 10.1016/j.jde.2018.06.001
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Solutions in mixed-norm Sobolev–Lorentz spaces to the initial value problem for the Navier–Stokes equations

D.Q. Khai and N.M. Tri
Journal of Mathematical Analysis and Applications 417 (2) 819 (2014)
DOI: 10.1016/j.jmaa.2014.03.068
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Uniform Local Existence for Inhomogeneous Rotating Fluid Equations

Mohamed Majdoub and Marius Paicu
Journal of Dynamics and Differential Equations 21 (1) 21 (2009)
DOI: 10.1007/s10884-008-9120-7
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On the influence of gravity on density-dependent incompressible periodic fluids

Van-Sang Ngo and Stefano Scrobogna
Journal of Differential Equations 267 (2) 1510 (2019)
DOI: 10.1016/j.jde.2019.02.011
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Uniform convergence for complex diffusion equation via a probabilistic approach and application

Olfa Bejaoui and Olfa Mahouachi
Mathematical Methods in the Applied Sciences 33 (15) 1856 (2010)
DOI: 10.1002/mma.1296
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Quality and Reliability of Large-Eddy Simulations II

Luigi C. Berselli, Traian Iliescu and Tamay Özgökmen
ERCOFTAC Series, Quality and Reliability of Large-Eddy Simulations II 16 399 (2011)
DOI: 10.1007/978-94-007-0231-8_36
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Articles citing this article

Cited article:

Fluids with anisotropic viscosity

This article has been cited by the following article(s):

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Derivation of limit equations for a singular perturbation of a 3D periodic Boussinesq system

Dispersive effects of weakly compressible and fast rotating inviscid fluids

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Horizontal Large Eddy Simulation of Stratified Mixing in a Lock-Exchange System

On the Global Well-posedness for the Boussinesq System with Horizontal Dissipation

Examples of dispersive effects in non-viscous rotating fluids

On the Global Wellposedness to the 3-D Incompressible Anisotropic Navier-Stokes Equations

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On the global well-posedness to the 3-D incompressible anisotropic magnetohydrodynamics equations

Global regularity for some classes of large solutions to the Navier-Stokes equations

Global Small Solutions to Three-Dimensional Incompressible Magnetohydrodynamical System

Global strong solution to the 3D incompressible magnetohydrodynamic system in the scaling invariant Besov–Sobolev-type spaces

A Uniqueness Result for the Navier--Stokes Equations with Vanishing Vertical Viscosity

Équation Périodique de Navier–Stokes sans Viscosité dans une Direction

Global Wellposed Problem for the 3-D Incompressible Anisotropic Navier-Stokes Equations in an Anisotropic Space

Global well-posedness for the 3D rotating Navier–Stokes equations with highly oscillating initial data

On some large global solutions to 3-D density-dependent Navier–Stokes system with slow variable: Well-prepared data

Global Small Solutions to an MHD-Type System: The Three-Dimensional Case

On the regularity criteria of the 2D Boussinesq equations with partial dissipation

A deterministic model for the propagation of turbulent oscillations

Global regularity for the Navier–Stokes equations with some classes of large initial data

Wellposedness for anisotropic rotating fluid equations

Inviscid limits for the Navier–Stokes equations with Navier friction boundary conditions

Global regularity for the 3D axisymmetric MHD Equations with horizontal dissipation and vertical magnetic diffusion

Global well-posedness for 3D Navier–Stokes equations with ill-prepared initial data

The inviscid limit of the incompressible anisotropic Navier–Stokes equations with the non-slip boundary condition

A solution to parabolic system with the fractional Laplacian

Étude asymptotique pour les fluides anisotropes en rotation rapide dans le cas périodique

Global wellposed problem for the 3-D incompressible anisotropic Navier–Stokes equations

Stability to the global large solutions of 3-D Navier–Stokes equations

Generalized Navier–Stokes equations with nonlinear anisotropic viscosity

GLOBAL EXISTENCE RESULTS FOR THE ANISOTROPIC BOUSSINESQ SYSTEM IN DIMENSION TWO

On 3D Navier–Stokes equations: Regularization and uniqueness by delays

Global large solutions to 3-D inhomogeneous Navier–Stokes system with one slow variable

On stochastic modified 3D Navier–Stokes equations with anisotropic viscosity

Evolution problems of Navier–Stokes type with anisotropic diffusion

A priori estimates for the 3D quasi-geostrophic system

Convergence results for MHD system

Anisotropic Regularity Conditions for the Suitable Weak Solutions to the 3D Navier–Stokes Equations

Existence and uniqueness of global solutions for the modified anisotropic 3D Navier−Stokes equations

THE VLASOV–POISSON SYSTEM WITH STRONG MAGNETIC FIELD IN QUASINEUTRAL REGIME

Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion

Global well-posedness of the three dimensional incompressible anisotropic Navier–Stokes system

Global regularity for generalized anisotropic Navier–Stokes equations

On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics with horizontal dissipation

Global small solutions of 2-D incompressible MHD system

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Vanishing vertical viscosity limit of anisotropic Navier–Stokes equation with no-slip boundary condition

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Uniform Local Existence for Inhomogeneous Rotating Fluid Equations

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