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

G. Deugoué; B. Jidjou Moghomye; T. Tachim Medjo

doi:10.3934/cpaa.2021010

Article Contents

2021, Volume 20, Issue 3: 1135-1170. Doi: 10.3934/cpaa.2021010

This issue Previous Article Boundary-Domain Integral Equations equivalent to an exterior mixed BVP for the variable-viscosity compressible Stokes PDEs Next Article The BSE concepts for vector-valued Lipschitz algebras

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

1.
Department of Mathematics and Computer Science, University of Dschang, P. O. BOX 67, Dschang, Cameroon
2.
Department of Mathematics, Florida International University, MMC, Miami, Florida 33199, USA

^* Corresponding author
^* Corresponding author

Received: August 31, 2019

Revised: September 30, 2020

Early access: February 2021

Published: March 2021

The first author is supported by the Fulbright Scholar Program Advanced Research and the Florida International University, 2019

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Abstract

In this paper, we consider a stochastic Allen-Cahn Navier-Stokes system in a bounded domain of $ \mathbb{R}^d, $ $ d = 2,3 $. 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.

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

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References

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