  We study the Ericksen-Leslie's parabolic-hyperbolic liquid crystal model in
compressible flow. Inspired by our study for incompressible case
\cite{Jiang-Luo-arXiv-2017} and some techniques from compressible Navier-Stokes
equations, we prove the local-in-time existence of the classical solution to
the system with finite initial energy, under some constraints on the Leslie
coefficients which ensure the basic energy law is dissipative. Furthermore,
with an additional assumption on the coefficients which provides a damping
effect, and the smallness of the initial energy, the global classical solution
can be established.
