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
收藏
页码：2175 / 2197
页数：23
相关论文
共 50 条
  • [21] Existence of weak solutions to the Ericksen-Leslie model for a general class of free energies
    Emmrich, Etienne
    Lasarzik, Robert
    MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2018, 41 (16) : 6492 - 6518
  • [22] ON DISSIPATIVE SOLUTIONS TO A SIMPLIFIED HYPERBOLIC ERICKSEN-LESLIE SYSTEM OF LIQUID CRYSTALS
    Cheng, Feng
    Jiang, Ning
    Luo, Yi-Long
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2021, 19 (01) : 175 - 192
  • [23] Global solvability of the inhomogeneous Ericksen-Leslie system with only bounded density
    De Anna, Francesco
    ANALYSIS AND APPLICATIONS, 2017, 15 (06) : 863 - 913
  • [24] EXISTENCE OF REGULAR SOLUTIONS TO AN ERICKSEN-LESLIE MODEL OF THE LIQUID CRYSTAL SYSTEM
    Dai, Mimi
    COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2015, 13 (07) : 1711 - 1740
  • [25] GLOBAL WELL-POSEDNESS FOR ERICKSEN-LESLIE SYSTEM WITH ZERO VISCOSITY
    Zhou, Jianfeng
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2024, 152 (05) : 2185 - 2197
  • [26] Existence, uniqueness and regularity for the stochastic Ericksen-Leslie equation
    De Bouard, Anne
    Hocquet, Antoine
    Prohl, Andreas
    NONLINEARITY, 2021, 34 (06) : 4057 - 4114
  • [27] ON Lp ESTIMATES FOR A SIMPLIFIED ERICKSEN-LESLIE SYSTEM
    Huang, Jinrui
    Wang, Wenjun
    Wen, Huanyao
    COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (03) : 1485 - 1507
  • [28] Existence and Uniqueness Theorems for the Two-Dimensional Ericksen-Leslie System
    Chechkin, Gregory A.
    Ratiu, Tudor S.
    Romanov, Maxim S.
    Samokhin, Vyacheslav N.
    JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2016, 18 (03) : 571 - 589
  • [29] On the uniqueness of weak solutions to the Ericksen-Leslie liquid crystal model in R2
    Li, Jinkai
    Titi, Edriss S.
    Xin, Zhouping
    MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, 2016, 26 (04): : 803 - 822
  • [30] WEAK-STRONG UNIQUENESS FOR THE GENERAL ERICKSEN-LESLIE SYSTEM IN THREE DIMENSIONS
    Emmrich, Etienne
    Lasarzik, Robert
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (09) : 4617 - 4635
12345