{
  "id": "2111.04792",
  "version": "v2",
  "published": "2021-11-08T20:02:00.000Z",
  "updated": "2022-09-01T21:02:48.000Z",
  "title": "Well-posedness for chemotaxis-fluid models in arbitrary dimensions",
  "authors": [
    "Gael Yomgne Diebou"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the Cauchy problem for the chemotaxis Navier-Stokes equations and the Keller-Segel-Navier-Stokes system. Local-in-time and global-in-time solutions satisfying fundamental properties such as mass conservation and nonnegativity preservation are constructed for low regularity data in $2$ and higher dimensions under suitable conditions. Our initial data classes involve a new scale of function space, that is $\\Y(\\rn)$ which collects divergence of vector-fields with components in the square Campanato space $\\mathscr{L}_{2,N-2}(\\rn)$, $N>2$ (and can be identified with the homogeneous Besov space $\\dot{B}^{-1}_{22}(\\rn)$ when $N=2$) and are shown to be optimal in a certain sense. Moreover, uniqueness criterion for global solutions is obtained under certain limiting conditions.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-09-01T21:02:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "92C17",
      "35Q35",
      "35K55",
      "35A02",
      "42B35"
    ],
    "keywords": [
      "arbitrary dimensions",
      "chemotaxis-fluid models",
      "well-posedness",
      "global-in-time solutions satisfying fundamental properties",
      "chemotaxis navier-stokes equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}