Approximation of a stochastic two-phase flow model by a splitting-up method

Abstract

<p style='text-indent:20px;'>In this paper, we consider a stochastic Allen-Cahn Navier-Stokes system in a bounded domain of <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^d, $\end{document}</tex-math></inline-formula> <inline-formula><tex-math id="M2">\begin{document}$ d = 2,3 $\end{document}</tex-math></inline-formula>. The system models the evolution of an incompressible isothermal mixture of binary fluids under the influence of stochastic external forces. We prove the existence of a global weak martingale solution. The proof is based on splitting-up method as well as some compactness method.