The low Mach number limit for the compressible flow of liquid crystals

In this paper, we are concerned with the compressible flow of liquid crystals. Based on the convergence-stability principle, it is shown that, for the Mach number sufficiently small, the Cauchy problem of compressible liquid crystal flow has a unique smooth solution on the (finite) time interval where the incompressible liquid crystal flow exists. Furthermore, it is justified that, as the Mach number tends to zero, the smooth solutions converge rigorously to those of the incompressible equations, and the sharp convergence orders are also obtained.