{
  "id": "0803.1788",
  "version": "v1",
  "published": "2008-03-12T14:45:35.000Z",
  "updated": "2008-03-12T14:45:35.000Z",
  "title": "The finite time blow-up for the Euler-Poisson equations in $\\Bbb R^n$",
  "authors": [
    "Dongho Chae"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove the finite time blow-up for $C^1$ solutions to the Euler-Poisson equations in $\\Bbb R^n$, $n\\geq 1$, with/without background density for initial data satisfying suitable conditions. We also find a sufficient condition for the initial data such that $C^3$ solution breaks down in finite time for the compressible Euler equations for polytropic gas flows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-12T14:45:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35B30"
    ],
    "keywords": [
      "finite time blow-up",
      "euler-poisson equations",
      "with/without background density",
      "initial data satisfying suitable conditions",
      "polytropic gas flows"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.1788C"
    }
  }
}