{
  "id": "1506.06076",
  "version": "v1",
  "published": "2015-06-19T16:21:01.000Z",
  "updated": "2015-06-19T16:21:01.000Z",
  "title": "A global existence result for a Keller-Segel type system with supercritical initial data",
  "authors": [
    "Daniele Bartolucci",
    "Daniele Castorina"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a parabolic-elliptic Keller-Segel type system, which is related to a simplified model of chemotaxis. Concerning the maximal range of existence of solutions, there are essentially two kinds of results: either global existence in time for general subcritical ($\\|\\rho_0\\|_1<8\\pi$) initial data, or blow--up in finite time for suitably chosen supercritical ($\\|\\rho_0\\|_1>8\\pi$) initial data with concentration around finitely many points. As a matter of fact there are no results claiming the existence of global solutions in the supercritical case. We solve this problem here and prove that, for a particular set of initial data which share large supercritical masses, the corresponding solution is global and uniformly bounded.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-19T16:21:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35K45",
      "35K57",
      "35K58"
    ],
    "keywords": [
      "global existence result",
      "supercritical initial data",
      "parabolic-elliptic keller-segel type system",
      "share large supercritical masses",
      "maximal range"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150606076B"
    }
  }
}