On the convergence of a stochastic 3D globally modified two-phase flow model

Theodore Tachim Medjo

doi:10.3934/dcds.2019016

Article Contents

2019, Volume 39, Issue 1: 395-430. Doi: 10.3934/dcds.2019016

This issue Previous Article Qualitative properties of positive solutions for mixed integro-differential equations Next Article An application of Moser's twist theorem to superlinear impulsive differential equations

On the convergence of a stochastic 3D globally modified two-phase flow model

Theodore Tachim Medjo

Department of Mathematics and Satistics, Florida International University, MMC, Miami, Florida 33199, USA

Received: February 28, 2018

Revised: June 30, 2018

Published: December 2018

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We study in this article a stochastic 3D globally modified Allen-Cahn-Navier-Stokes model in a bounded domain. We prove the existence and uniqueness of a strong solutions. The proof relies on a Galerkin approximation, as well as some compactness results. Furthermore, we discuss the relation between the stochastic 3D globally modified Allen-Cahn-Navier-Stokes equations and the stochastic 3D Allen-Cahn-Navier-Stokes equations, by proving a convergence theorem. More precisely, as a parameter $N$ tends to infinity, a subsequence of solutions of the stochastic 3D globally modified Allen-Cahn-Navier-Stokes equations converges to a weak martingale solution of the stochastic 3D Allen-Cahn-Navier-Stokes equations.

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Mathematics Subject Classification: 35R60, 35Q35, 60H15, 76M35, 86A05.

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