Existence and uniqueness of the solution of a Boussinesq  system   with nonlinear dissipation

Dominique Blanchard; Nicolas Bruyère; Olivier Guibé

doi:10.3934/cpaa.2013.12.2213

Article Contents

2013, Volume 12, Issue 5: 2213-2227. Doi: 10.3934/cpaa.2013.12.2213

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Existence and uniqueness of the solution of a Boussinesq system with nonlinear dissipation

1.
Laboratoire de Mathématiques Raphaël Salem, UMR CNRS 6085, Université de Rouen, Avenue de l'université, BP12, 76801 Saint Étienne du Rouvray cedex
2.
Laboratoire de Mathématiques Raphaël Salem, UMR 6085 CNRS - Université de Rouen, Avenue de l'Université, BP.12, 76801 Saint-Étienne du Rouvray

Received: July 31, 2011

Revised: November 30, 2012

Published: August 2013

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Abstract

We give existence and uniqueness results of the weak-renormalized solution for a class of nonlinear Boussinesq's systems. The main tools rely on regularity results for the Navier-Stokes equations with precise estimates on the solution with respect to the data in dimension $2$ and on the techniques involved for renormalized solutions of parabolic problems.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 35D05, 35D30, 76D03.

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