Global Strong Solution to the Density-Dependent 2-D Liquid Crystal Flows

Abstract

The initial-boundary value problem for the density-dependent flow of nematic crystals is studied in a 2-D bounded smooth domain. For the initial density away from vacuum, the existence and uniqueness is proved for the global strong solution with the large initial velocity $u_0$ and small $\nabla d_0$. We also give a regularity criterion of the problem with the Dirichlet boundary condition $u=0$, $d=d_0$ on $\partial \mathrm{\Omega }$.