Open AccessGlobal weak solutions to the stochastic Ericksen–Leslie system in dimension two
Author(s) -
Hengrong Du,
Changyou Wang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021187
Subject(s) - compact space , martingale (probability theory) , mathematics , bounded function , convergence (economics) , type (biology) , liquid crystal , pure mathematics , mathematical analysis , physics , ecology , economics , biology , economic growth , optics
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.