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 u0 and small Δ d0. We also give a regularity criterion Δ d Ε L p (0, T; Lp (Ω)) (2 / q) + (2 / p) = 1, 2 < q ≤ ∞ of the problem with the Dirichlet boundary condition u = 0, d = d0 on ∂ Ω. © 2013 Yong Zhou et al.