{
  "id": "math/0405197",
  "version": "v2",
  "published": "2004-05-11T17:48:05.000Z",
  "updated": "2005-02-18T09:31:31.000Z",
  "title": "Global existence results for nonlinear Schrodinger equations with quadratic potentials",
  "authors": [
    "Remi Carles"
  ],
  "comment": "Some typos fixed, Proposition 1.1 extended. Final version to appear in DCDS",
  "journal": "Discrete Contin. Dyn. Syst. 13 (2005), no. 2, 385-398",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that no finite time blow up can occur for nonlinear Schroedinger equations with quadratic potentials, provided that the potential has a sufficiently strong repulsive component. This is not obvious in general, since the energy associated to the linear equation is not positive. The proof relies essentially on two arguments: global in time Strichartz estimates, and a refined analysis of the linear equation, which makes it possible to use continuity arguments and to control the nonlinear effects.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-02-18T09:31:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A05",
      "35B30",
      "35B35"
    ],
    "keywords": [
      "nonlinear schrodinger equations",
      "global existence results",
      "quadratic potentials",
      "linear equation",
      "finite time blow"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5197C"
    }
  }
}