Weak solution of a stochastic 2D Ericksen–Leslie model driven by jump noise

Abstract

We investigate a stochastic 2D Ericksen–Leslie model with a multiplicative noise of Lévy type. The system models the dynamic of nematic liquid crystals under the influence of stochastic external forces and stretching effects. We prove the existence of a weak martingale solution of the system. The proof of the existence is based on a classical Galerkin approximation as well as some compactness methods. We also prove the pathwise uniqueness of the weak solution when the stretching effect is neglected.