{
  "id": "2204.03531",
  "version": "v1",
  "published": "2022-04-07T15:59:08.000Z",
  "updated": "2022-04-07T15:59:08.000Z",
  "title": "Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media",
  "authors": [
    "Edriss S. Titi",
    "Saber Trabelsi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider three-dimensional (3D) Boussinesq convection system of an incompressible fluid in a closed sample of a porous medium. Specifically, we introduce and analyze a 3D Brinkman-Forchheimer-B\\'enard convection problem describing the behavior of an incompressible fluid in a porous medium between two plates heated from the bottom and cooled from the top. We show the existence and uniqueness of global in-time solutions, and the existence of absorbing balls in $L^2$ and $H^1$. Eventually, we comment on the applicability of a data assimilation algorithm to our system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-07T15:59:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q30",
      "35Q35",
      "76B03",
      "86A10",
      "93C20",
      "37C50",
      "76B75",
      "34D06"
    ],
    "keywords": [
      "three-dimensional brinkman-forchheimer-bénard convection model",
      "porous medium",
      "global well-posedness",
      "3d brinkman-forchheimer-benard convection problem",
      "data assimilation algorithm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}