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

Jishan Fan; Tohru Ozawa

doi:10.3934/krm.2009.2.293

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2009, Volume 2, Issue 2: 293-305. Doi: 10.3934/krm.2009.2.293

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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
2.
Department of Applied Physics, Waseda University, Tokyo, 169-8555

Received: March 31, 2008

Revised: December 31, 2008

Published: May 2009

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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.

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