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ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 935045, 10 pages
doi:10.5402/2012/935045
Research Article
Regularity Criterion for the 3D Nematic Liquid Crystal Flows
1Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan
Received 17 January 2012; Accepted 14 February 2012
Academic Editors: A. Carpio, Y. Liu, and G. A. Seregin
Copyright © 2012 Jishan Fan and Tohru Ozawa. 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 study the hydrodynamic theory of liquid crystals. We prove a logarithmically improved regularity criterion for two simplified Ericksen-Leslie systems.