Speaker: Hengrong Du (Vanderbilt University)

Abstract:  In this talk, we present a method for establishing the global existence of weak martingale solutions to the simplified stochastic Ericksen—Leslie system. This system models the hydrodynamics of nematic liquid crystals driven by Wiener-type noises on two-dimensional bounded domains. Our approach involves constructing solutions through the convergence of Ginzburg—Landau approximations. To achieve this convergence, we first employ the concentration-cancellation method for the Ericksen stress tensor fields, based on a Pohozaev-type argument. We then use the Skorokhod compactness theorem, which is built upon uniform energy estimates. This is joint work with Changyou Wang (Purdue).