{
  "id": "1212.6816",
  "version": "v1",
  "published": "2012-12-31T04:33:12.000Z",
  "updated": "2012-12-31T04:33:12.000Z",
  "title": "The defocusing $\\dot{H}^{1/2}$-critical NLS in high dimensions",
  "authors": [
    "Jason Murphy"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the defocusing $\\dot{H}^{1/2}$-critical nonlinear Schr\\\"odinger equation in dimensions $d\\geq 5$. In the spirit of Kenig and Merle [Trans. Amer. Math. Soc. 362 (2010), 1937--1962], we combine a concentration-compactness approach with the Lin--Strauss Morawetz inequality to prove that if a solution $u$ is bounded in $\\dot{H}^{1/2}$ throughout its lifespan, then $u$ is global and scatters.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-31T04:33:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "high dimensions",
      "critical nls",
      "defocusing",
      "lin-strauss morawetz inequality",
      "concentration-compactness approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.6816M"
    }
  }
}