Weak solution of a stochastic 3D Cahn-Hilliard-Navier-Stokes model driven by jump noise

Abstract

We investigate a stochastic 2D and 3D Cahn-Hilliard-Navier-Stokes system with a multiplicative noise of Lévy type. The model consists of the Navier-Stokes equations for the velocity, coupled with a Cahn-Hilliard system for the order (phase) parameter. We prove that the system the existence of weak martingale solution for both 2D and 3D cases. The proof of the existence is based on a classical Galerkin approximation as well as some compactness methods. In the 2D case, we prove the pathwise uniqueness of the weak solution.