不可压双曲型液晶的Ericksen-Leslie方程的大Ericksen数的极限的形式分析

摘要/Abstract

摘要：

该文考虑了参数化的液晶的不可压双曲型的Ericksen-Leslie方程.形式上，让参数消失该文证明了这个极限方程存在一个局部的经典解.更进一步，该文形式上得出一个关于这个参数化的液晶的双曲型方程和极限方程的解的误差估计，这对应的是关于它们的经典解在$L$²空间中的一个形式上的能量估计.

关键词: 液晶, Ericksen-Leslie方程, 大Ericksen数极限

Abstract:

In this paper, we consider the parameterized incompressible hyperbolic Ericksen-Leslie system of liquid crystals. Formally, letting the parameter vanish, we prove that the limit system admits a local classical solution. Moreover, we formally obtained an estimate on the difference between the parameterized Ericksen-Leslie's incompressible hyperbolic liquid crystal model and the corresponding limit system, which corresponds to a formal energy estimate of the difference of the classical solutions in $L^2$ space.

Key words: Liquid crystals, Ericksen-Leslie system, Classical solution, Large Ericksen number limit

中图分类号:

O175.25

程峰. 不可压双曲型液晶的Ericksen-Leslie方程的大Ericksen数的极限的形式分析[J]. 数学物理学报, 2021, 41(1): 126-141.

Feng Cheng. A Formal Analysis on the Large Ericksen Number Limit for the Incompressible Hyperbolic Ericksen-Leslie System of Liquid Crystals[J]. Acta mathematica scientia,Series A, 2021, 41(1): 126-141.

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