On a stochastic Cahn-Hilliard-Brinkman model
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.
Cite
@article{arxiv.2601.06698,
title = {On a stochastic Cahn-Hilliard-Brinkman model},
author = {Z. Brzeźniak and A. Ndongmo Ngana and T. Tachim Medjo},
journal= {arXiv preprint arXiv:2601.06698},
year = {2026}
}