{
  "id": "1110.0915",
  "version": "v1",
  "published": "2011-10-05T07:55:52.000Z",
  "updated": "2011-10-05T07:55:52.000Z",
  "title": "An inhomogeneous, $L^2$ critical, nonlinear Schrödinger equation",
  "authors": [
    "François Genoud"
  ],
  "journal": "Z. Anal. Anwend. 31 (2012), 283-290",
  "categories": [
    "math.AP"
  ],
  "abstract": "An inhomogeneous nonlinear Schr\\\"odinger equation is considered, that is invariant under $L^2$ scaling. The sharp condition for global existence of $H^1$ solutions is established, involving the $L^2$ norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in finite time.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-05T07:55:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35A01",
      "35B44",
      "35C06"
    ],
    "keywords": [
      "nonlinear schrödinger equation",
      "inhomogeneous",
      "sharp condition",
      "finite time",
      "ground state"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.0915G"
    }
  }
}