We consider a stochastic diffuse interface model which describes the motion of an incompressible isothermal mixture of two immiscible fluids under the influence of stochastic external forces in a bounded domain of R d , d = 2, 3. The model consists of the stochastic Navier-Stokes equations coupled with a nonlocal Cahn-Hilliard equation. We prove the existence of a global weak martingale solution via a numerical scheme based on splitting-up method.
In this paper we study the numerical approximation of the stochastic Cahn–Hilliard–Navier–Stokes system on a bounded polygonal domain of $\mathbb{R}^{d}$, $d=2,3$. We propose and analyze an algorithm based on the finite element method and a semiimplicit Euler scheme in time for a fully discretization. We prove that the proposed numerical scheme satisfies the discrete mass conservative law, has finite energies and constructs a weak martingale solution of the stochastic Cahn–Hilliard–Navier–Stokes system when the discretization step (both in time and in space) tends to zero.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.