{
  "id": "2311.18590",
  "version": "v1",
  "published": "2023-11-30T14:34:54.000Z",
  "updated": "2023-11-30T14:34:54.000Z",
  "title": "Global Solution of 3-D Patlak-Keller-Segal Model with Couette flow in whole space",
  "authors": [
    "Shijin Deng",
    "Binbin Shi",
    "Weike Wang"
  ],
  "comment": "24 page",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider both parabolic-elliptic Patlak-Keller-Segel model and parabolic-parabolic Patlak-Keller-Segel model in the background of a Couette flow with spatial variables in $\\mathbb{R}^3$. It is proved that for both parabolic-elliptic and parabolic-parabolic cases, a Couette flow with a sufficiently large amplitude prevents the blow-up of solutions. This result is totally different from either the classical Patlak-Keller-Segel model or the case with a large shear flow and the periodic spatial variable $x$; for those two cases, the solution may blow up. Here, we apply Green's function method to capture the suppression of blow-up and prove the global existence of the solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-30T14:34:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35Q92",
      "76F25",
      "65M80"
    ],
    "keywords": [
      "couette flow",
      "global solution",
      "patlak-keller-segal model",
      "parabolic-elliptic patlak-keller-segel model",
      "parabolic-parabolic patlak-keller-segel model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}