The Oberbeck-Boussinesq approximation in critical spacesReport as inadecuate

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1 LAMA - Laboratoire d-Analyse et de Mathématiques Appliquées 2 Department of Mathematical Sciences

Abstract : 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.

Author: Raphaël Danchin - Lingbing He -



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