首页|The Oberbeck-Boussinesq approximation in critical spaces

The Oberbeck-Boussinesq approximation in critical spaces

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In this paper we study the validity of the so-called Oberbeck-Boussinesq approximation for compressible viscous perfect gases in the whole three-dimensional space. Both the cases of fluids with positive heat conductivity and zero conductivity are considered. For small perturbations of a constant equilibrium, we establish the global existence of unique strong solutions in a critical regularity functional framework. Next, taking advantage of Strichartz estimates for the associated system of acoustic waves, and of uniform estimates with respect to the Mach number, we obtain all-time convergence to the Boussinesq system with a explicit decay rate.

compressible fluidsNavier-Stokeslow Mach numberlow Froude numbercritical regularity

Raphaeel Danchin、Lingbing He

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Universite Paris-Est, LAMA (UMR 8050), UPEMLV, UPEC, CNRS, Institut Universitaire de France, 61 avenue du Gdneral de Gaulle, 94010 Creteil Cedex, France

Department of Mathematical Sciences, Tsinghua University, Beijing, China

2013

10.3233/ASY-131170

Asymptotic analysis

Asymptotic analysis

SCI
ISSN：0921-7134
年,卷(期)：2013.84(1/2)
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