Table of Contents
International Journal of Partial Differential Equations
Volume 2014 (2014), Article ID 213083, 5 pages
http://dx.doi.org/10.1155/2014/213083
Research Article

MHD Equations with Regularity in One Direction

School of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China

Received 3 July 2014; Accepted 6 October 2014; Published 27 October 2014

Academic Editor: Antonin Novotny

Copyright © 2014 Zujin Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the 3D MHD equations and prove that if one directional derivative of the fluid velocity, say, , with , , then the solution is in fact smooth.  This improves previous results greatly.