Z.J. Zhang, Regularity criterion for the system modeling the flow of liquid crystals via the direction of velocity, Comm. Appl. Nonlinear Anal., 17 (2010), No.3, 55-60.

Abstract

We consider sufficient conditions for the regularity of weak solutions to the system modeling the flow of liquid crystals. It is proved that we can control the direction of velocity and the direction of liquid crystals to ensure smoothness. Our result extend the case for incompressible Navier-Stokes equations.