Table of Contents
ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 248473, 7 pages
http://dx.doi.org/10.5402/2012/248473
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.

Linked References

  1. F. Lin and C. Liu, β€œStatic and dynamic theories of liquid crystals,” Journal of Partial Differential Equations, vol. 14, no. 4, pp. 289–330, 2001. View at Google Scholar
  2. H. Triebel, Theory of Function Spaces. II, vol. 84, Birkhäuser, Basel, Switzerland, 1992. View at Publisher Β· View at Google Scholar
  3. H. Brézis and T. Gallouet, β€œNonlinear Schrödinger evolution equations,” Nonlinear Analysis, vol. 4, no. 4, pp. 677–681, 1980. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  4. H. Brézis and S. Wainger, β€œA note on limiting cases of Sobolev embeddings and convolution inequalities,” Communications in Partial Differential Equations, vol. 5, no. 7, pp. 773–789, 1980. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  5. T. Ozawa, β€œOn critical cases of Sobolev's inequalities,” Journal of Functional Analysis, vol. 127, no. 2, pp. 259–269, 1995. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  6. H. Kozono, T. Ogawa, and Y. Taniuchi, β€œThe critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations,” Mathematische Zeitschrift, vol. 242, no. 2, pp. 251–278, 2002. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. T. Kato and G. Ponce, β€œCommutator estimates and the Euler and Navier-Stokes equations,” Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 891–907, 1988. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  8. J. Fan and T. Ozawa, β€œOn regularity criterion for the 2D wave maps and the 4D biharmonic wave maps,” in Current Advances in Nonlinear Analysis and Related Topics, vol. 32 of GAKUTO International Series Mathematical Sciences and Applications, pp. 69–83, Gakkōtosho, Tokyo, Japan, 2010. View at Google Scholar Β· View at Zentralblatt MATH