{
  "id": "1503.04425",
  "version": "v1",
  "published": "2015-03-15T13:42:10.000Z",
  "updated": "2015-03-15T13:42:10.000Z",
  "title": "Propagation of moments and uniqueness of weak solution to Vlasov-Poisson-Fokker-Planck system",
  "authors": [
    "Ze Li",
    "Lifeng Zhao"
  ],
  "comment": "18 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove the uniqueness of weak solution to Vlasov-Poisson-Fokker-Planck system in $C([0,T]; L^p)$, by assuming the solution has local bounded density which trends to infinite with a \"reasonable\" rate as $t$ trends zero. And particularly as a corollary, we get uniqueness of weak solution with initial data $f_0$ satisfying $f_0|v|^2\\in L^1$, which solves the uniqueness of solutions with finite energy. In addition, we prove that the moments in velocity propagate for any order higher than 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-15T13:42:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q83",
      "35Q84"
    ],
    "keywords": [
      "weak solution",
      "vlasov-poisson-fokker-planck system",
      "uniqueness",
      "propagation",
      "order higher"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}