On the existence, uniqueness and regularity of strong solutions to a stochastic 2D Cahn–Hilliard-Magnetohydrodynamic model

Author:

Tadmon Calvin1ORCID,Deugoué Gabriel2,Awo Kougang Salvador2

Affiliation:

1. Committed Mathematics Team, Research Unit in Mathematics and Applications ; and Departement of Mathematics and Computer Science , Faculty of Science , 362702 University of Dschang , P.O. Box 67 , Dschang , Cameroon ; and Institute of Mathematics University of Mainz, Staudingersweg 9, 55128 Mainz, Germany

2. Committed Mathematics Team, Research Unit in Mathematics and Applications ; and Departement of Mathematics and Computer Science , Faculty of Science , 362702 University of Dschang , P.O. Box 67 , Dschang , Cameroon

Abstract

Abstract We investigate a stochastic coupled model of the Cahn–Hilliard equations and the stochastic magnetohydrodynamic equations in a bounded domain of 2 {\mathbb{R}^{2}} . The model describes the flow of the mixture of two incompressible and immiscible fluids under the influence of an electromagnetic field with stochastic perturbations. We prove the existence, uniqueness and regularity of a probabilistic strong solution. The proof of the existence is based on the Galerkin approximation, the stopping time technique and some weak convergence principles in functional analysis.

Publisher

Walter de Gruyter GmbH

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