Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 248473, 7 pages
Research Article

Continuation Criterion for the 2D Liquid Crystal Flows

1Department of Applied Mathematics, Nanjing Forestry University, Nanjing 210037, China
2Department of Applied Physics, Waseda University, Tokyo 169-8555, Japan

Received 16 December 2011; Accepted 17 January 2012

Academic Editors: A. Montes-Rodriguez and T.-P. Tsai

Copyright Β© 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.


We consider the 2D liquid crystal systems, which consists of Navier-Stokes system coupled with wave maps or biharmonic wave maps, respectively. By logarithmic Sobolev inequalities, we obtain a blow-up criterion βˆ‡π‘‘,πœ•π‘‘π‘‘βˆˆπΏ1̇𝐡(0,𝑇;0∞,∞(ℝ2)) for the case with wave maps, and we prove the existence of a global-in-time strong solutions for the case with biharmonic wave maps.