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

共 50 条

[41] On global well-posedness and decay of 3D Ericksen-Leslie system
Zhao, Xiufang
Duan, Ning
AIMS MATHEMATICS, 2021, 6 (11): : 12660 - 12679
[42] CONVERGENCE OF THE GINZBURG-LANDAU APPROXIMATION FOR THE ERICKSEN-LESLIE SYSTEM
Feng, Zhewen
Hong, Min-Chun
Mei, Yu
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2020, 52 (01) : 481 - 523
[43] Convergence of the ginzburg-landau approximation for the ericksen-leslie system
Feng, Zhewen
Hong, Min-Chun
Mei, Yu
SIAM Journal on Mathematical Analysis, 2020, 52 (01): : 481 - 523
[44] Blow-up Criteria of Strong Solutions to the Ericksen-Leslie System in R3
Hong, Min-Chun
Li, Jinkai
Xin, Zhouping
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2014, 39 (07) : 1284 - 1328
[45] Large Ericksen number limit for the 2D general Ericksen-Leslie system
Cheng, Feng
Jiang, Ning
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2022, 65
[46] Blow-up criteria of the simplified Ericksen-Leslie system
Chen, Zhengmao
Wu, Fan
BOUNDARY VALUE PROBLEMS, 2023, 2023 (01)
[47] On unique solvability of the full three-dimensional Ericksen-Leslie system
Chechkin, Gregory A.
Ratiu, Tudor S.
Romanov, Maxim S.
Samokhin, Vyacheslav N.
COMPTES RENDUS MECANIQUE, 2016, 344 (07): : 459 - 463
[48] Global existence of weak solution for the 2-D Ericksen–Leslie system
Meng Wang
Wendong Wang
Calculus of Variations and Partial Differential Equations, 2014, 51 : 915 - 962
[49] WELL-POSEDNESS OF THE FULL ERICKSEN-LESLIE SYSTEM IN BOUNDED DOMAINS
Wang, Huaijie
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2024, 29 (10): : 3980 - 4001
[50] Analysis and Numerical Approximation of Energy-Variational Solutions to the Ericksen-Leslie Equations
Lasarzik, Robert
Reiter, Maximilian E. V.
ACTA APPLICANDAE MATHEMATICAE, 2023, 184 (01)

← 1 2 3 4 5 →