A regularity criterion for the nematic liquid crystal flows. (English) Zbl 1191.82112

Summary: A logarithmically improved regularity criterion for the 3D nematic liquid crystal flows is established.


82D30 Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses)
76A15 Liquid crystals


liquid crystal
Full Text: DOI EuDML


[1] de Gennes PG: The Physics of Liquid Crystals. Oxford University Press, Oxford, Mass, USA; 1974. · Zbl 0295.76005
[2] Lin F-H, Liu C: Nonparabolic dissipative systems modeling the flow of liquid crystals. Communications on Pure and Applied Mathematics 1995, 48(5):501-537. 10.1002/cpa.3160480503 · Zbl 0842.35084
[3] Sun H, Liu C: On energetic variational approaches in modeling the nematic liquid crystal flows. Discrete and Continuous Dynamical Systems. Series A 2009, 23(1-2):455-475. · Zbl 1156.76007
[4] He C, Xin Z: On the regularity of weak solutions to the magnetohydrodynamic equations. Journal of Differential Equations 2005, 213(2):235-254. 10.1016/j.jde.2004.07.002 · Zbl 1072.35154
[5] Zhou Y: Remarks on regularities for the 3D MHD equations. Discrete and Continuous Dynamical Systems. Series A 2005, 12(5):881-886. · Zbl 1068.35117
[6] Zhou Y: Regularity criteria for the generalized viscous MHD equations. Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 2007, 24(3):491-505. · Zbl 1130.35110
[7] Montgomery-Smith S: Conditions implying regularity of the three dimensional Navier-Stokes equation. Applications of Mathematics 2005, 50(5):451-464. 10.1007/s10492-005-0032-0 · Zbl 1099.35086
[8] Fan J, Gao H: Regularity conditions for the 3D Navier-Stokes equations. Quarterly of Applied Mathematics 2009, 67(1):195-199. · Zbl 1163.35453
[9] Zhou Y, Fan J: Logarithmically improved regularity criteria for the generalized Navier-Stokes and related equations. Submitted · Zbl 1282.35296
[10] Zhou Y, Gala S: Logarithmically improved regularity criteria for the Navier-Stokes equations in multiplier spaces. Journal of Mathematical Analysis and Applications 2009, 356(2):498-501. 10.1016/j.jmaa.2009.03.038 · Zbl 1172.35063
[11] Kato T, Ponce G: Commutator estimates and the Euler and Navier-Stokes equations. Communications on Pure and Applied Mathematics 1988, 41(7):891-907. 10.1002/cpa.3160410704 · Zbl 0671.35066
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