Regular Global existence of strong solutions to the isentropic compressible nematic liquid crystal equations in a cuboid domain

In this paper, we study the initial-boundary value problem of three-dimensional compressible nematic liquid crystal equations in a cuboid domain. We prove that the strong solution exists globally in the time provided that both the initial L(1)norm of the density ||rho(0)|| L(1)and the initial L-3-norm of the gradient of orientation field ||Vd(0)|| L-3 for nematic liquid crystal flow are small enough. The main tools of proving the global well-posedness are some time-weighted a priori estimates designed for the compressible nematic liquid crystal equations.