{
  "annotation_id": "e8e3354f-8a85-4d6d-bf53-67bb13e1d6ff",
  "date_created": "2026-02-17T05:53:08.450000Z",
  "date_modified": "2026-02-17T05:53:08.450000Z",
  "file_hash": "8d4985bc80ef6b9624ae01e8830a6fa212ea4fdae33f86b2352cf22f023e9216",
  "private": false,
  "record": {
    "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.",
    "arxiv_id": "2601.06698",
    "authors": [
      "Z. Brze\u017aniak",
      "A. Ndongmo Ngana",
      "T. Tachim Medjo"
    ],
    "categories": [
      "math.PR",
      "math.AP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On a stochastic Cahn-Hilliard-Brinkman model",
    "url": "https://arxiv.org/abs/2601.06698",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ba0829d1-6887-4372-99c0-bcfcfa877efb",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}