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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 319585, 8 pages
On Regularity Criteria for the Two-Dimensional Generalized Liquid Crystal Model
Department of Mathematics, Zhejiang Normal University, Jinhua , Zhejiang 321004, China
Received 5 May 2014; Revised 27 June 2014; Accepted 1 July 2014; Published 15 July 2014
Academic Editor: Yongli Song
Copyright © 2014 Yanan Wang and Zaihong Jiang. 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.
- P. G. de Gennes, The Physics of Liquid Crystals, Oxford University Press, Oxford, UK, 1974.
- J. L. Ericksen, “Hydrostatic theory of liquid crystals,” Archive for Rational Mechanics and Analysis, vol. 9, pp. 371–378, 1962.
- F. M. Leslie, “Some constitutive equations for liquid crystals,” Archive for Rational Mechanics and Analysis, vol. 28, no. 4, pp. 265–283, 1968.
- D. Coutand and S. Shkoller, “Well-posedness of the full Ericksen-Leslie model of nematic liquid crystals,” Comptes Rendus de l'Académie des Sciences I: Mathematics, vol. 333, no. 10, pp. 919–924, 2001.
- F. 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.
- F. Lin and C. Liu, “Existence of solutions for the Ericksen-Leslie system,” Archive for Rational Mechanics and Analysis, vol. 154, no. 2, pp. 135–156, 2000.
- H. Sun and C. Liu, “On energetic variational approaches in modeling the nematic liquid crystal flows,” Discrete and Continuous Dynamical Systems A, vol. 23, no. 1-2, pp. 455–475, 2009.
- Y. Zhou and J. Fan, “A regularity criterion for the nematic liquid crystal flows,” Journal of Inequalities and Applications, vol. 2010, Article ID 589697, 9 pages, 2010.
- J. Fan and T. Ozawa, “Regularity criterion for the incompressible viscoelastic fluid system,” Houston Journal of Mathematics, vol. 37, no. 2, pp. 627–636, 2011.
- J. Fan, G. Nakamura, and Y. Zhou, “Global regularity for the 2D liquid crystal model with mixed partial viscosity”.
- Y. Wang, Y. Zhou, A. Alsaedi, T. Hayat, and Z. Jiang, “Global regularity for the incompressible 2D generalized liquid crystal model with fractional diffusions,” Applied Mathematics Letters, vol. 35, pp. 18–23, 2014.
- Y. Jin, Y. Zhou, and M. Zhu, “Global existence of solutions to the 2D incompressible liquid crystal ow with fractional diffusion,” preprint.
- Y. Zhou, J. Fan, and G. Nakamura, “Global strong solution to the density-dependent 2-D liquid crystal flows,” Abstract and Applied Analysis, vol. 2013, Article ID 947291, 5 pages, 2013.
- Z. Jiang and Y. Zhou, “On regularity criteria for the 2D generalized MHD system,” preprint.
- H. Kozono and Y. Taniuchi, “Bilinear estimates in BMO and the Navier-Stokes equations,” Mathematische Zeitschrift, vol. 235, no. 1, pp. 173–194, 2000.