{
  "id": "1603.08912",
  "version": "v1",
  "published": "2016-03-29T19:50:01.000Z",
  "updated": "2016-03-29T19:50:01.000Z",
  "title": "The focusing cubic NLS with inverse-square potential in three space dimensions",
  "authors": [
    "Rowan Killip",
    "Jason Murphy",
    "Monica Visan",
    "Jiqiang Zheng"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the focusing cubic nonlinear Schr\\\"odinger equation with inverse-square potential in three space dimensions. We identify a sharp threshold between scattering and blowup, establishing a result analogous to that of Duyckaerts, Holmer, and Roudenko for the standard focusing cubic NLS. We also prove failure of uniform space-time bounds at the threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-29T19:50:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "space dimensions",
      "inverse-square potential",
      "uniform space-time bounds",
      "standard focusing cubic nls",
      "sharp threshold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160308912K"
    }
  }
}