  In this paper, we investigate the Cauchy problem for the compressible nematic
liquid crystal flows in three-dimensional whole space. First of all, we
establish the time decay rates for compressible nematic liquid crystal flows by
the method of spectral analysis and energy estimates. Furthermore, we enhance
the convergence rates for the higher-order spatial derivatives of density,
velocity and director. Finally, the time decay rates of mixed space-time
derivatives of solution are also established.
