A blow-up criterion for the 3D compressible MHD equations

Ming Lu; Yi Du; Zheng-An Yao; Zujin Zhang

doi:10.3934/cpaa.2012.11.1167

Article Contents

2012, Volume 11, Issue 3: 1167-1183. Doi: 10.3934/cpaa.2012.11.1167

This issue Previous Article One dimensional symmetry of solutions to some anisotropic quasilinear elliptic equations in the plane Next Article Analysis of a contact problem for electro-elastic-visco-plastic materials

A blow-up criterion for the 3D compressible MHD equations

1.
Department of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275
2.
Department of Mathematical Sciences, South China Normal University, Guangzhou, 510631
3.
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275

Received: November 30, 2010

Revised: March 31, 2011

Published: April 2012

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Abstract

In this paper, we study the 3D compressible magnetohydrodynamic equations. We extend the well-known Serrin's blow-up criterion(see [32]) for the 3D incompressible Navier-Stokes equations to the 3D compressible magnetohydrodynamic equations. In addition, initial vacuum is allowed in our case.

Keywords:

Blow-up criterion,
strong solutions,
3D compressible magnetohydrodynamic equations.

Mathematics Subject Classification: Primary: 35Q35, 35Q80; Secondary: 76N10.

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