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.
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页码：2175 / 2197
页数：23
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