On a stochastic Cahn-Hilliard-Brinkman model

Z. Brzeźniak; A. Ndongmo Ngana; T. Tachim Medjo

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arXiv · 2601.06698

On a stochastic Cahn-Hilliard-Brinkman model

Z. Brzeźniak·A. Ndongmo Ngana·T. Tachim Medjo

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Abstract

In this paper, we consider a stochastic version of the Cahn-Hilliard-Brinkman model in a smooth two- or three-dimensional domain with dynamical boundary conditions. The system describes creeping two-phase flows and is basically a coupling of the Brinkman equation for the velocity field that governs the flow through the porous media coupled with convective Cahn-Hilliard equations for the phase field, both with two independent sources of randomness given by general multiplicative-type Wiener noises in the Cahn-Hilliard equations. The existence of a weak solution, both in the probabilistic and PDEs sense, is proved. Our construction of a solution is based on the classical Faedo-Galerkin approximation, the Yosida approximation and uses a compactness method. Our paper is the first attempt to generalize the paper \cite{Colli+Knopf+Schimperna+Signor_2024} to a stochastic setting.

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Z. Brzeźniak, A. Ndongmo Ngana, T. Tachim Medjo. 2026-01-10. On a stochastic Cahn-Hilliard-Brinkman model. https://arxiv.org/abs/2601.06698

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