Fluids with anisotropic viscosity

Jean-Yves Chemin; Benoît Desjardins; Isabelle Gallagher; Emmanuel Grenier

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 34, Issue: 2, page 315-335
  • ISSN: 0764-583X

Abstract

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Motivated by rotating fluids, we study incompressible fluids with anisotropic viscosity. We use anisotropic spaces that enable us to prove existence theorems for less regular initial data than usual. In the case of rotating fluids, in the whole space, we prove Strichartz-type anisotropic, dispersive estimates which allow us to prove global wellposedness for fast enough rotation.

How to cite

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Chemin, Jean-Yves, et al. "Fluids with anisotropic viscosity." ESAIM: Mathematical Modelling and Numerical Analysis 34.2 (2010): 315-335. <http://eudml.org/doc/197442>.

@article{Chemin2010,
abstract = { Motivated by rotating fluids, we study incompressible fluids with anisotropic viscosity. We use anisotropic spaces that enable us to prove existence theorems for less regular initial data than usual. In the case of rotating fluids, in the whole space, we prove Strichartz-type anisotropic, dispersive estimates which allow us to prove global wellposedness for fast enough rotation. },
author = {Chemin, Jean-Yves, Desjardins, Benoît, Gallagher, Isabelle, Grenier, Emmanuel},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Navier-Stokes equations; Rotating fluids; Strichartz estimates.; Strichartz-type anisotropic dispersive estimates; rotating fluids; incompressible fluids; anisotropic viscosity; anisotropic spaces; existence theorem; global well-posedness},
language = {eng},
month = {3},
number = {2},
pages = {315-335},
publisher = {EDP Sciences},
title = {Fluids with anisotropic viscosity},
url = {http://eudml.org/doc/197442},
volume = {34},
year = {2010},
}

TY - JOUR
AU - Chemin, Jean-Yves
AU - Desjardins, Benoît
AU - Gallagher, Isabelle
AU - Grenier, Emmanuel
TI - Fluids with anisotropic viscosity
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 34
IS - 2
SP - 315
EP - 335
AB - Motivated by rotating fluids, we study incompressible fluids with anisotropic viscosity. We use anisotropic spaces that enable us to prove existence theorems for less regular initial data than usual. In the case of rotating fluids, in the whole space, we prove Strichartz-type anisotropic, dispersive estimates which allow us to prove global wellposedness for fast enough rotation.
LA - eng
KW - Navier-Stokes equations; Rotating fluids; Strichartz estimates.; Strichartz-type anisotropic dispersive estimates; rotating fluids; incompressible fluids; anisotropic viscosity; anisotropic spaces; existence theorem; global well-posedness
UR - http://eudml.org/doc/197442
ER -

References

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  6. J. -Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids, preprint of Université d'Orsay (1999).  
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  13. E. Grenier and N. Masmoudi, Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations22, No. 5-6, (1997) 953-975.  
  14. D. Iftimie, La résolution des équations de Navier-Stokes dans des domaines minces et la limite quasigéostrophique. Thèse de l'Université Paris 6 (1997).  
  15. D. Iftimie, The resolution of the Navier-Stokes equations in anisotropic spaces. Revista Matematica Ibero-Americana15 (1999) 1-36.  
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  19. M. Sablé-Tougeron, Régularité microlocale pour des problèmes aux limites non linéaires. Annales de l'Institut Fourier36 (1986) 39-82.  

Citations in EuDML Documents

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  1. Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier, Ekman boundary layers in rotating fluids
  2. Jean-Yves Chemin, Benoît Desjardins, Isabelle Gallagher, Emmanuel Grenier, Ekman boundary layers in rotating fluids
  3. Christophe Cheverry, Cascade of phases in turbulent flows
  4. Jamel Ben Ameur, Ridha Selmi, Study of Anisotropic MHD system in Anisotropic Sobolev spaces
  5. Christophe Cheverry, Sur la propagation de quasi-singularités
  6. Christophe Cheverry, Sur un problème de stabilité posé en optique géométrique non linéaire surcritique
  7. Marius Paicu, Fluides incompressibles horizontalement visqueux

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