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

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 del d(0). We also give a regularity criterion del d epsilon L-p(0,T; L-q (Omega))((2/q)) = 1,2 < q <= infinity) of the problem with the Dirichlet boundary condition u = 0, d = d(0) on delta Omega