{
  "id": "1112.4452",
  "version": "v2",
  "published": "2011-12-19T20:08:10.000Z",
  "updated": "2014-04-16T03:49:17.000Z",
  "title": "Interaction Morawetz estimate for the magnetic Schrödinger equation and applications",
  "authors": [
    "James Colliander",
    "Magdalena Czubak",
    "Jeonghun Lee"
  ],
  "comment": "23 pages; Added some remarks in the introduction and more details in the proof of LWP and GWP, fixed typos. To appear in DIE",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish an interaction Morawetz estimate for the magnetic Schr\\\"odinger equation for $n\\geq 3$ under certain smallness conditions on the gauge potentials, but with almost optimal decay. As an application, we prove global wellposedness and scattering in $H^1$ for the cubic defocusing magnetic Schr\\\"odinger equation for $n = 3.$",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-16T03:49:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interaction morawetz estimate",
      "magnetic schrödinger equation",
      "application",
      "smallness conditions",
      "gauge potentials"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.4452C"
    }
  }
}