The Oberbeck-Boussinesq approximation in critical spaces

2013/04/16 by Raphaël Danchin, Danchin, Raphaël, Ling-Bing He +1
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1304.4376

openalex publication_date 2013/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Global Well-Posedness Issues for the Inviscid Boussinesq System with Yudovich’s Type Data

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