{
  "id": "1809.09831",
  "version": "v1",
  "published": "2018-09-26T07:21:58.000Z",
  "updated": "2018-09-26T07:21:58.000Z",
  "title": "Large global solutions for nonlinear Schrödinger equations I, mass-subcritical cases",
  "authors": [
    "Marius Beceanu",
    "Qingquan Deng",
    "Avy Soffer",
    "Yifei Wu"
  ],
  "comment": "36 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we consider the nonlinear Schr\\\"odinger equation, $$ i\\partial_{t}u+\\Delta u= \\mu|u|^p u, \\quad (t,x)\\in \\mathbb{R}^{d+1}, $$ with $\\mu=\\pm1, p>0$. In this work, we consider the mass-subcritical cases, that is, $p\\in (0,\\frac4d)$. We prove that under some restrictions on $d,p$, any radial initial data in the critical space $\\dot H^{s_c}(\\mathbb{R}^d)$ with compact support, implies global well-posedness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-26T07:21:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A01"
    ],
    "keywords": [
      "nonlinear schrödinger equations",
      "large global solutions",
      "mass-subcritical cases",
      "radial initial data",
      "implies global well-posedness"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}