Journal of Applied Mathematics
Volume 2011 (2011), Article ID 456547, 12 pages
http://dx.doi.org/10.1155/2011/456547
Research Article

Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

Yu-Zhu Wang and Zigao Chen

School of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, China

Received 20 March 2011; Accepted 26 June 2011

Academic Editor: Ch Tsitouras

Copyright © 2011 Yu-Zhu Wang and Zigao Chen. 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

Regularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some 𝑇 > 0 , if ∫ 𝑇 0 ‖ 𝑣 𝑥 3 ‖ 𝜌 𝐿 𝜚 𝑑 𝑡 < ∞ , where 3 / 𝜚 + 2 / 𝜌 ≤ 1 and 𝜚 ≥ 3 , then the solution ( 𝑣 , 𝑤 ) can be extended smoothly beyond 𝑡 = 𝑇 . The derivative 𝑣 𝑥 3 can be substituted with any directional derivative of 𝑣 .