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

TL;DR

This paper establishes the existence of martingale solutions for the complex three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Levy processes, using advanced probabilistic and analytical methods.

Contribution

It introduces a novel approach to prove the existence of solutions for these equations driven by Levy processes, combining Galerkin approximation, stopping times, and the Jakubowski-Skorokhod theorem.

Findings

Existence of martingale solutions is proven.

Method combines Galerkin approximation with probabilistic compactness techniques.

Results extend understanding of stochastic Navier-Stokes equations driven by Levy noise.

Abstract

In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by L\'evy process 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, stopping time, the compactness method and the Jakubowski-Skorokhod theorem.