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

  • Calvin Tadmon ORCID logo EMAIL logo , Gabriel Deugoué and Salvador Awo Kougang
Published/Copyright: September 3, 2024

Abstract

We investigate a stochastic coupled model of the Cahn–Hilliard equations and the stochastic magnetohydrodynamic equations in a bounded domain of 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.

MSC 2020: 35R60; 60H15; 76W05

Acknowledgements

The authors are very thankful to the editor and the reviewers for their thoughtful reading and constructive suggestions that greatly improved the initial version of this paper. Calvin Tadmon acknowledges good working conditions at the University of Mainz, Germany, where this paper was revised during a research stay supported by the Alexander von Humboldt Foundation.

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Received: 2023-11-25
Revised: 2024-07-20
Accepted: 2024-07-26
Published Online: 2024-09-03

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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