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Remarks on the regularity criteria for the 3D MHD equations in the multiplier spaces

Zujin Zhang1*, Xiqin Ouyang2, Dingxing Zhong1 and Shulin Qiu1

Author Affiliations

1 School of Mathematics and Computer Sciences, Gannan Normal University, Ganzhou, Jiangxi, 341000, P.R. China

2 College of Mathematics, Gannan Institute of Education, Ganzhou, Jiangxi, 341000, P.R. China

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Boundary Value Problems 2013, 2013:270  doi:10.1186/1687-2770-2013-270

Published: 12 December 2013

Abstract

In this paper, we consider the regularity criteria for the 3D MHD equations. It is proved that if

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or

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then the solution actually is smooth. This extends the previous results given by Guo and Gala (Anal. Appl. 10:373-380, 2013), Gala (Math. Methods Appl. Sci. 33:1496-1503, 2010).

MSC: 35B65, 35Q35, 76D03.

Keywords:
MHD equations; regularity criteria; regularity of solutions