{
  "id": "1006.1375",
  "version": "v3",
  "published": "2010-06-07T21:04:15.000Z",
  "updated": "2016-07-27T15:02:11.000Z",
  "title": "Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr{ö}dinger equation when $d = 2$",
  "authors": [
    "Benjamin Dodson"
  ],
  "comment": "75 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove that the defocusing, cubic nonlinear Schr{\\\"o}dinger initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R}^{2})$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in \\cite{CKSTT4}. Since we are considering an $L^{2}$ - critical initial value problem we will localize to low frequencies.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-18T21:52:49.000Z",
      "comment": "85 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2016-07-27T15:02:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "global well-posedness",
      "nonlinear schr",
      "dinger equation",
      "initial value problem",
      "localized interaction morawetz estimate similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 75,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1006.1375D"
    }
  }
}