A refined blow up criterion for the nematic liquid crystals

Abstract

In this paper, we refine the blow-up criterion of Huang-Wang [T. Huang, C.Y. Wang, Blow up criterion for nematic liquid crystal flows,

A remark on blow up criterion of three-dimensional nematic liquid crystal flows

“…The problem (1), (2) has great challenge and attracts many Mathematician's interest. Some interesting results have been established, we may refer to [2], [9], [12] , [24], [25], [28] and [29]. The existence of strong solution to liquid crystals system in critical Besov space and a criterion which is similar to Serrins criterion on regularity of weak solution to Navier-Stokes equations have been established by Hao and Liu [9].…”

“…More precisely, they proved that 0 < T < +∞ is the maximal time interval iff T 0 ( ∇ × u L ∞ + ∇d 2 L ∞ )dt = ∞. This blow up criterion was refined in [29]. Very recently, Zhang, Tan and Wu [28] obtained a blow up criterion of smooth solutions.…”