Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows

In this paper, we prove the unique existence of global strong solutions and decay estimates for the simplified Ericksen–Leslie system describing compressible nematic liquid crystal flows in RN, 3≤N≤7. Firstly, we rewrite the system in Lagrange coordinates, and secondly, we prove the global well-posedness for the transformed system, which is the main task in this paper. The proof is based on the maximal Lp-Lq regularity and the Lp-Lq decay estimates to the linearized problem.

在本文中，我们证明了描述在\(R^N\)（\(3\leq N\leq7\)）中可压缩向列型液晶流的简化Ericksen - Leslie系统全局强解的唯一存在性以及衰减估计。首先，我们在拉格朗日坐标下重写该系统，其次，我们证明变换后的系统的全局适定性，这是本文的主要任务。证明基于线性化问题的最大\(L^p - L^q\)正则性以及\(L^p - L^q\)衰减估计。