A stochastic Allen–Cahn–Navier–Stokes model with inertial effects driven by multiplicative noise of jump type

Abstract

AbstractWe consider a stochastic Allen–Cahn–Navier–Stokes equations with inertial effects and multiplicative noise of jump type in a bounded domain , , driven by a multiplicative noise. The existence of a global weak martingale solution is proved under non‐Lipschitz assumptions on the coefficients. The construction of the solution is based on the Faedo–Galerkin approximation, compactness method and the Skorokhod representation theorem.