{
  "id": "1811.04378",
  "version": "v1",
  "published": "2018-11-11T09:36:51.000Z",
  "updated": "2018-11-11T09:36:51.000Z",
  "title": "Large global solutions for nonlinear Schrödinger equations II, mass-supercritical, energy-subcritical cases",
  "authors": [
    "Marius Beceanu",
    "Qingquan Deng",
    "Avy Soffer",
    "Yifei Wu"
  ],
  "comment": "59 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 $p>0, \\mu=\\pm1$. In this work, we consider the defocusing mass-supercritical, energy-subcritical cases, that is, $p\\in (\\frac4d,\\frac4{d-2}),\\mu=\\pm1$. We prove that under some restrictions on $d,p$, any radial initial data in the rough space $H^{s_0}(\\mathbb R^d), s_0<s_c$ with the support away from the origin, there exists an incoming/outgoing decomposition, such that the initial data in the outgoing part leads to the global well-posedness and scattering in the forward time; while the initial data in the incoming part leads to the global well-posedness and scattering in the backward time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-11T09:36:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55"
    ],
    "keywords": [
      "large global solutions",
      "nonlinear schrödinger equations",
      "energy-subcritical cases",
      "global well-posedness",
      "radial initial data"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 59,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}