  In this article, we consider the Ericksen-Leslie's hyperbolic system for
compressible liquid crystal model in three spatial dimensions. Global
regularity for small and smooth initial data near equilibrium is proved for the
case that the system is a nonlinear coupling of compressible Navier-Stokes
equations with wave map to $\mathbb{S}^2$. Our argument is a combination of
vector field method and Fourier analysis. The main strategy to prove global
regularity relies on an interplay between the control of high order energies
and decay estimates, which is based on the idea inspired by the method of
space-time resonances. In particular the different behaviors of the decay
properties of the density and velocity field for compressible fluids at
different frequencies play a key role.
