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 flow, a simplified version of Ericksen–Leslie system modeling the hydrodynamic evolution of nematic liquid crystals, in dimensions two and three. More precisely, 0 < T * < + ∞ is the maximal time interval iff (i) for n = 3, ; and (ii) for n = 2, .