Journal ArticleGlobal weak solutions to the stochastic Ericksen-Leslie system in dimension twoDu, Hengrong; Wang, ChangyouWe 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.2022-04-0110339536Discrete and continuous dynamical systems42number 52175–21971078-0947https://doi.org/10.3934/dcds.20211872101224National Science Foundation