Large Time Asymptotic Behavior of Classical Solutions to the 3D Compressible Nematic Liquid Crystal Flows with Vacuum

Abstract

This paper concerns the large time asymptotic decay with rates of the global classical solutions in the three spatial dimensions with vacuum as far field density. we prove that the L2$L^{2}$-norm of both the pressure, the gradient of the velocity and the gradient of orientation decay in time with a rate tź12$t^{-\frac{1}{2}}$, and the gradient of the vorticity and the effective viscous flux decay faster than themselves. When d$d$ is a constant vector, the large time decay rates (1.12) are the same as Li and Xin (Global well-posedness and decay asymptotic behavior of classical solution to the compressible Navier-Stokes equations with vacuum, 2003).