Global weak solutions to the stochastic Ericksen–Leslie system in dimension two

<p style='text-indent:20px;'>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.</p>