Martingale solutions to stochastic nonlocal Cahn–Hilliard–Navier–Stokes equations with multiplicative noise of jump type

Abstract

Abstract In this paper, we are interested in proving the existence of a weak martingale solution of the stochastic nonlocal Cahn–Hilliard–Navier–Stokes system driven by a pure jump noise in both 2D and 3D bounded domains. Our goal is achieved by using the classical Faedo–Galerkin approximation, a compactness method and a version of the Skorokhod embedding theorem for nonmetric spaces. In the 2D case, we prove the pathwise uniqueness of the solution and use the Yamada–Watanabe classical result to derive the existence of a strong solution.