{
  "id": "math/0606389",
  "version": "v1",
  "published": "2006-06-16T12:21:22.000Z",
  "updated": "2006-06-16T12:21:22.000Z",
  "title": "Optimal gradient estimates and asymptotic behaviour for the Vlasov-Poisson system with small initial data",
  "authors": [
    "Hyung Ju Hwang",
    "Alan D. Rendall",
    "Juan J. L. Velazquez"
  ],
  "comment": "37 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The Vlasov-Poisson system describes interacting systems of collisionless particles. For solutions with small initial data in three dimensions it is known that the spatial density of particles decays like $t^{-3}$ at late times. In this paper this statement is refined to show that each derivative of the density which is taken leads to an extra power of decay so that in $N$ dimensions for $N\\ge 3$ the derivative of the density of order $k$ decays like $t^{-N-k}$. An asymptotic formula for the solution at late times is also obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-06-16T12:21:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B40"
    ],
    "keywords": [
      "small initial data",
      "optimal gradient estimates",
      "vlasov-poisson system",
      "asymptotic behaviour",
      "late times"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......6389H"
    }
  }
}