{
  "id": "1902.10736",
  "version": "v1",
  "published": "2019-02-27T19:10:16.000Z",
  "updated": "2019-02-27T19:10:16.000Z",
  "title": "On Patlak-Keller-Segel system for several populations: a gradient flow approach",
  "authors": [
    "Debabrata Karmakar",
    "Gershon Wolansky"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the global in time existence of solutions to the parabolic-elliptic Patlak-Keller-Segel system of multi-species populations. We prove that if the initial mass satisfies an appropriate notion of sub-criticality, then the system has a solution defined for all time. We explore the gradient flow structure in the Wasserstein space to study the question of existence. Moreover, we show that the obtained solution satisfies energy dissipation inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-27T19:10:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gradient flow approach",
      "solution satisfies energy dissipation inequality",
      "populations",
      "gradient flow structure",
      "initial mass satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}