{
  "id": "0806.1373",
  "version": "v3",
  "published": "2008-06-09T05:59:33.000Z",
  "updated": "2009-08-06T07:32:18.000Z",
  "title": "Global well-posedness for the $L^2$ critical Hartree equation on $\\bbr^n$, $n\\ge 3$",
  "authors": [
    "Myeongju Chae",
    "Soonsik Kwon"
  ],
  "comment": "Some minor correction on Error estimate made",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the initial value problem for the L^2-critical defocusing Hartree equation in R^n, n \\ge 3. We show that the problem is globally well posed in H^s(R^n) when 1>s> \\frac{2(n-2)}{3n-4}$. We use the \"I-method\" combined with a local in time Morawetz estimate for the smoothed out solution.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-06T07:32:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "critical hartree equation",
      "global well-posedness",
      "initial value problem",
      "time morawetz estimate",
      "defocusing hartree equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.1373C"
    }
  }
}