Abstract: In this talk, we will consider the Ericksen-Leslie’s hyperbolic system for compressible liquid crystal model in three spatial dimensions, which is a nonlinear coupling of compressible Navier-Stokes equations with wave map to S^2. Global regularity for small and smooth initial data near the equilibrium is proved. 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. Joint work with Ning Jiang, Yi-Long Luo, and Lifeng Zhao.