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Global well-posedness of non-isothermal inhomogeneous nematic liquid crystal flows
Discrete and Continuous Dynamical Systems-Series B ( IF 1.2 ) Pub Date : 2020-05-15 , DOI: 10.3934/dcdsb.2020161
Dongfen Bian , , Yao Xiao , ,

In this paper, we consider the initial-boundary value problem to the non-isothermal incompressible liquid crystal system with both variable density and temperature. Global well-posedness of strong solutions is established for initial data being small perturbation around the equilibrium state. As the tools in the proof, we establish the maximal regularities of the linear Stokes equations and parabolic equations with variable coefficients and a rigid lemma for harmonic maps on bounded domains. This paper also generalizes the result in [5] to the inhomogeneous case.

中文翻译:

非等温不均匀向列液晶流的整体适定性

在本文中,我们考虑了具有可变密度和温度的非等温不可压缩液晶系统的初边值问题。建立强解决方案的全局适定性,是为了使初始数据在平衡状态附近具有较小的扰动。作为证明中的工具,我们建立了线性Stokes方程和具有可变系数和刚性引理的抛物型方程的最大正则性,用于有界域上的调和映射。本文还对[5]到不均匀的情况。
更新日期:2020-05-15
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