Article Dans Une Revue Asymptotic Analysis Année : 2013

The Oberbeck-Boussinesq approximation in critical spaces

Résumé

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 uids 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.

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hal-00795419 , version 1 (16-04-2013)

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Raphaël Danchin, Lingbing He. The Oberbeck-Boussinesq approximation in critical spaces. Asymptotic Analysis, 2013, 84, pp.61-102. ⟨hal-00795419⟩
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