Incompressible limit of the compressible nematic liquid crystal flows in a bounded domain with perfectly conducting boundary

In this paper, we study the asymptotic behavior of the regular solution to a simplified Ericksen-Leslie model for the compressible nematic liquid crystal flow in a bounded smooth domain in R-2 as the Mach number tends to zero. The evolution system consists of the compressible Navier-Stokes equations coupled with the transported heat flow for the averaged molecular orientation. We suppose that the Navier-Stokes equations are characterized by a Navier's slip boundary condition, while the transported heat flow is subject to Neumann boundary condition. By deriving a differential inequality with certain decay property, the low Mach limit of the solutions is verified for all time, provided that the initial data are well-prepared. (C) 2019 Elsevier Inc. All rights reserved.