On the Weak Solutions to a Stochastic 2D Simplified Ericksen-Leslie Model

Abstract

We study in this article a stochastic version of a 2D Ericksen-Leslie systems. The system model the dynamic of nematic liquid crystals under the influence of stochastic external forces and stretching effects. We prove the existence of a probabilistic weak solutions. The proof relies on a reformulation of the model proposed in Gong et al. (Nonlinearity 28(10), 3677–3694 2015) as well as a Galerkin approximation and some compactness results. We also prove the pathwise uniqueness of the weak solution when the stretching effect is neglected.