GLOBAL WEAK SOLUTIONS TO THE STOCHASTIC ERICKSEN-LESLIE SYSTEM IN DIMENSION TWO

被引：0

作者：

Du, Hengrong ^{[1
]}

Wang, Changyou ^{[2
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

[2] Purdue Univ, Dept Math, W Lafayette, IN 47907 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2022年 / 42卷 / 05期

基金：

美国国家科学基金会;

关键词：

Stochastic nematic liquid crystal flow; Wiener process; Brownian motion; LIQUID-CRYSTALS DRIVEN; EXISTENCE; MARTINGALE; REGULARITY; EQUATIONS; NOISE; FLOW;

D O I：

10.3934/dcds.2021187

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the global existence of weak martingale solutions to the simplified stochastic Ericksen-Leslie system modeling the nematic liquid crystal flow driven by Wiener-type noises on the two-dimensional bounded domains. The construction of solutions is based on the convergence of Ginzburg- Landau approximations. To achieve such a convergence, we first utilize the concentration-cancellation method for the Ericksen stress tensor fields based on a Pohozaev type argument, and then the Skorokhod compactness theorem, which is built upon uniform energy estimates.

引用

页码：2175 / 2197

页数：23

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