{
  "id": "1010.0040",
  "version": "v2",
  "published": "2010-10-01T00:20:53.000Z",
  "updated": "2011-03-18T21:49:50.000Z",
  "title": "Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schrödinger equation when $d = 1$",
  "authors": [
    "Benjamin Dodson"
  ],
  "comment": "48 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove that the defocusing, quintic nonlinear Schr\\\"odinger initial value problem is globally well-posed and scattering for $u_{0} \\in L^{2}(\\mathbf{R})$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in [11]. Since we are considering an $L^{2}$ - critical initial value problem we will localize to low frequencies.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-03-18T21:49:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "global well-posedness",
      "initial value problem",
      "frequency localized interaction morawetz estimate",
      "localized interaction morawetz estimate similar"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1010.0040D"
    }
  }
}