{
  "id": "2011.13904",
  "version": "v1",
  "published": "2020-11-27T18:46:05.000Z",
  "updated": "2020-11-27T18:46:05.000Z",
  "title": "Global well-posedness and long-time behavior of the fractional NLS",
  "authors": [
    "Mouhamadou Sy",
    "Xueying Yu"
  ],
  "comment": "35 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish probabilistic global well-posedness results for the cubic Schr\\\"odinger equation with any fractional power of the Laplacian in all dimensions. We consider both low and high regularities on both radial (in dimension $\\geq 2$) and periodic settings (in all dimensions). For the high regularities, an {\\it Inviscid - Infinite dimensional (IID) limit} is used while we use the Skorokhod representation for low regularity global well-posedness. The IID limit is presented in details as an independent method. Also, our discussion mainly focuses on equations with energy supercritical nonlinearities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-27T18:46:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "long-time behavior",
      "fractional nls",
      "high regularities",
      "low regularity global well-posedness",
      "establish probabilistic global well-posedness results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}