{
  "id": "1001.1474",
  "version": "v3",
  "published": "2010-01-10T04:48:28.000Z",
  "updated": "2010-06-14T06:12:56.000Z",
  "title": "Scattering threshold for the focusing nonlinear Klein-Gordon equation",
  "authors": [
    "Slim Ibrahim",
    "Nader Masmoudi",
    "Kenji Nakanishi"
  ],
  "comment": "56 pages, no figure, minor corrections, to appear in Analysis & PDE",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show scattering versus blow-up dichotomy below the ground state energy for the focusing nonlinear Klein-Gordon equation, in the spirit of Kenig-Merle for the $H^1$ critical wave and Schr\\\"odinger equations. Our result includes the $H^1$ critical case, where the threshold is given by the ground state for the massless equation, and the 2D square-exponential case, where the mass for the ground state may be modified, depending on the constant in the sharp Trudinger-Moser inequality. The main difficulty is lack of scaling invariance both in the linear and nonlinear terms.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2010-06-14T06:12:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70",
      "35B40",
      "35B44",
      "47J30"
    ],
    "keywords": [
      "focusing nonlinear klein-gordon equation",
      "scattering threshold",
      "sharp trudinger-moser inequality",
      "ground state energy",
      "2d square-exponential case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1001.1474I"
    }
  }
}