Regularity criteria for a magnetohydrodynamic-$\alpha$ model

Yong Zhou; Jishan Fan

doi:10.3934/cpaa.2011.10.309

Article Contents

2011, Volume 10, Issue 1: 309-326. Doi: 10.3934/cpaa.2011.10.309

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Regularity criteria for a magnetohydrodynamic-$\alpha$ model

Yong Zhou^1, and
Jishan Fan^2,

1.
Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang 321004
2.
Department of Applied Mathematics, Nanjing Forestry University, Nanjing, 210037

Received: January 2010

Revised: June 2010

Published: January 2011

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Abstract

We study the $n$-dimensional magnetohydrodynamic-$\alpha$ (MHD-$\alpha$) model in the whole space. Various regularity criteria are established. When $n=4$, uniqueness of weak solutions is also proved. As a corollary, the strong solution to this model exists globally, as $n \leq 4$.

Keywords:

Primary: 35B40,
76D03.

Mathematics Subject Classification: Primary: 35B40, 76D03.

Citation:

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