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Fluids with anisotropic viscosity

Published online by Cambridge University Press:  15 April 2002

Jean-Yves Chemin ,
Benoît Desjardins ,
Isabelle Gallagher  and
Emmanuel Grenier
Jean-Yves Chemin
Affiliation:
Laboratoire d'Analyse Numérique, CNRS UMR 7598, Université Paris 6, place Jussieu, 75005 Paris, France.
Benoît Desjardins
Affiliation:
CEA, BP 12, 91680 Bruyères-le Châtel, France.
Isabelle Gallagher
Affiliation:
CNRS UMR 8628 , Université Paris Sud, Bâtiment 425, 91405 Orsay Cedex, France.
Emmanuel Grenier
Affiliation:
UMPA (CNRS UMR 5669), E.N.S. Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
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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.

Keywords

Navier-Stokes equationsRotating fluidsStrichartz estimates.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 34 , Issue 2: Special issue for R. Teman's 60th birthday , March 2000 , pp. 315 - 335
Copyright
© EDP Sciences, SMAI, 2000

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