Global Existence of Strong Solutions for Incompressible Hydrodynamic Flow of Liquid Crystals With Vacuum

Shijin Ding, Jinrui Huang, Fengguang Xia

We consider the Cauchy problem for incompressible hydrodynamic flow of nematic liquid crystals in three dimensions. We prove the global existence and uniqueness of the strong solutions with nonnegative $\rho_0$ and small initial data.