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Kinetic and Related Models (KRM)
 

Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model

Pages: 293 - 305, Volume 2, Issue 2, June 2009      doi:10.3934/krm.2009.2.293

 
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Jishan Fan - Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, China (email)
Tohru Ozawa - Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan (email)

Abstract: We prove some regularity conditions for the MHD equations with partial viscous terms and the Leray-$\alpha$-MHD model. Since the solutions to the Leray-$\alpha$-MHD model are smoother than that of the original MHD equations, we are able to obtain better regularity conditions in terms of the magnetic field $B$ only.

Keywords:  MHD equations, regularity criterion, Leray-$\alpha$-MHD model, interpolation inequality in Besov spaces.
Mathematics Subject Classification:  35Q35, 76D03.

Received: April 2008;      Revised: January 2009;      Available Online: May 2009.