Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier–Stokes equations driven by Lévy processes

Abstract

In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier–Stokes equations driven by Lévy processes consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are considered in a bounded domain. We obtain the existence of martingale solutions. The construction of the solution is based on the classical Galerkin approximation method, the stopping times, the stochastic compactness method and the Jakubowski–Skorokhod theorem.