Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows
Global Well-Posedness for the Compressible Nematic Liquid Crystal Flows
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DOI：
10.3390/math11010181
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发表时间：
2022-12
期刊：
影响因子：
2.4
通讯作者：
M. Murata
中科院分区：
文献类型：
--
作者：
M. Murata
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。
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.