{
  "id": "0708.0849",
  "version": "v1",
  "published": "2007-08-06T21:48:35.000Z",
  "updated": "2007-08-06T21:48:35.000Z",
  "title": "The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher",
  "authors": [
    "Rowan Killip",
    "Monica Visan",
    "Xiaoyi Zhang"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schr\\\"odinger equation $iu_t + \\Delta u = \\pm |u|^{4/d} u$ for large spherically symmetric L^2_x(R^d) initial data in dimensions $d\\geq 3$. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-08-06T21:48:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "mass-critical nonlinear schrödinger equation",
      "radial data",
      "dimensions",
      "ground state",
      "focusing case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.0849K"
    }
  }
}