On a stochastic Cahn-Hilliard-Brinkman model
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arXiv
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2026
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| _version_ | 1866915720630108160 |
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| author | Brzeźniak, Z. Ngana, A. Ndongmo Medjo, T. Tachim |
| author_facet | Brzeźniak, Z. Ngana, A. Ndongmo Medjo, T. Tachim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_06698 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On a stochastic Cahn-Hilliard-Brinkman model Brzeźniak, Z. Ngana, A. Ndongmo Medjo, T. Tachim Probability Analysis of PDEs 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. |
| title | On a stochastic Cahn-Hilliard-Brinkman model |
| topic | Probability Analysis of PDEs |
| url | https://arxiv.org/abs/2601.06698 |