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June  2009, 2(2): 293-305. doi: 10.3934/krm.2009.2.293

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

Jishan Fan 1, and  Tohru Ozawa 2,

1. 

Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037, China
2. 

Department of Applied Physics, Waseda University, Tokyo, 169-8555, Japan

Received  April 2008 Revised  January 2009 Published  May 2009

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, interpolation inequality in Besov spaces., Leray-$\alpha$-MHD model.
Mathematics Subject Classification: 35Q35, 76D0.
Citation: Jishan Fan, Tohru Ozawa. Regularity criteria for the magnetohydrodynamic equations with partial viscous terms and the Leray-$\alpha$-MHD model. Kinetic and Related Models, 2009, 2 (2) : 293-305. doi: 10.3934/krm.2009.2.293
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