Martingale solutions to a stochastic smectic-A liquid crystal model with multiplicative noise of jump type

Abstract

In this paper, we are interested in proving the existence of a weak martingale solution of the stochastic smectic-A liquid crystal system driven by a pure jump noise in both 2D and 3D bounded domains. We prove the existence of a global weak martingale solution under some non-Lipschitz assumptions on the coefficients. The construction of the solution is based on a Faedo–Galerkin approximation, a compactness method and the Skorokhod representation theorem. In the two-dimensional case, we prove the pathwise uniqueness of the weak solution, which implies the existence of a unique probabilistic strong solution.