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Communications on Pure and Applied Analysis (CPAA)
 

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

Pages: 1167 - 1183, Volume 11, Issue 3, May 2012      doi:10.3934/cpaa.2012.11.1167

 
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Ming Lu - Department of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China (email)
Yi Du - Department of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China (email)
Zheng-An Yao - Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China (email)
Zujin Zhang - Department of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China (email)

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.

Received: December 2010;      Revised: April 2011;      Available Online: December 2011.

 References