Long-time behavior of solution for the compressible nematic liquid crystal flows in R3

In this paper, we investigate the global existence and long-time behavior of classical solution for the compressible nematic liquid crystal flows in three-dimensional whole space. First of all, the global existence of classical solution is established under the condition that the initial data are close to the constant equilibrium state in HN(R3) (N≥3)-framework. Then, one establishes algebraic time decay for the classical solution by weighted energy method. Finally, the algebraic decay rate of classical solution in Lp(R3)-norm with 2≤p≤∞ and optimal decay rate of their spatial derivative in L2(R3)-norm are obtained if the initial perturbation belong to L1(R3) additionally.