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ISRN Mathematical Analysis
Volume 2012 (2012), Article ID 935045, 10 pages
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.
- J. L. Ericksen, “Conservation laws for liquid crystals,” Transactions of The Society of Rheology, vol. 5, pp. 23–34, 1961.
- J. Ericksen, “Continuum theory of nematic liquid crystals,” Res Mechanica, vol. 21, pp. 381–392, 1987.
- J. L. Ericksen, “Liquid crystals with variable degree of orientation,” Archive for Rational Mechanics and Analysis, vol. 113, no. 2, pp. 97–120, 1990.
- F. Leslie, Theory of Flow Phenomenum in Liquid Crystals, vol. 4, Springer, New York, NY, USA, 1979.
- F.-H. Lin and C. Liu, “Nonparabolic dissipative systems modeling the flow of liquid crystals,” Communications on Pure and Applied Mathematics, vol. 48, no. 5, pp. 501–537, 1995.
- J. Fan and B. Guo, “Regularity criterion to some liquid crystal models and the Landau-Lifshitz equations in ,” Science in China A, vol. 51, no. 10, pp. 1787–1797, 2008.
- J. Fan and T. Ozawa, “Regularity criteria for a simplified Ericksen-Leslie system modeling the flow of liquid crystals,” Discrete and Continuous Dynamical Systems A, vol. 25, no. 3, pp. 859–867, 2009.
- J. Fan, H. Gao, and B. Guo, “Regularity criteria for the Navier-Stokes-Landau-Lifshitz system,” Journal of Mathematical Analysis and Applications, vol. 363, no. 1, pp. 29–37, 2010.
- H. Kozono and Y. Shimada, “Bilinear estimates in homogeneous Triebel-Lizorkin spaces and the Navier-Stokes equations,” Mathematische Nachrichten, vol. 276, pp. 63–74, 2004.
- T. Kato and G. Ponce, “Commutator estimates and the Euler and Navier-Stokes equations,” Communications on Pure and Applied Mathematics, vol. 41, no. 7, pp. 891–907, 1988.
- S. Machihara and T. Ozawa, “Interpolation inequalities in Besov spaces,” Proceedings of the American Mathematical Society, vol. 131, no. 5, pp. 1553–1556, 2003.
- Y. Meyer, “Oscillating patterns in some nonlinear evolution equations,” in Mathematical Foundation of Turbulent Viscous Flows, vol. 1871 of Lecture Notes in Mathematics, pp. 101–187, Springer, Berlin, Germany, 2006.