SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Open Badges Research

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

For all author emails, please log on.

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

Published: 12 December 2013


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

<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/270/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/270/mathml/M1">View MathML</a>


<a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/270/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/270/mathml/M2">View MathML</a>

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.

MHD equations; regularity criteria; regularity of solutions