Blow up criterion for nematic liquid crystal flows

Abstract

In this paper, we establish a blow up criterion for the short time classical solution of the nematic liquid crystal ow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals, in dimensions two and three. More precisely, $0<T_{\ast }<+\infty$ is the maximal time interval iff (i) for $n=3$, $|\omega |+|\nabla d{|}^2\notin L_t^1{L}_x^{\infty }({\mathbb{R}}^3\times [0,T_{\ast }])$, and (ii) for $n=2$, $|\nabla {|}^2\notin L_t^1{L}_x^{\infty }({\mathbb{R}}^2\times [0,T_{\ast }])$.

9 pages

Cited by in corpus (2)

• Blow up criterion for compressible nematic liquid crystal flows in dimension three
• Global Well-Posedness with Large Oscillations and Vacuum to the Three-Dimensional Equations of Compressible Nematic Liquid Crystal Flows