{
  "id": "0911.4745",
  "version": "v1",
  "published": "2009-11-25T01:36:46.000Z",
  "updated": "2009-11-25T01:36:46.000Z",
  "title": "Dynamics for the energy critical nonlinear wave equation in high dimensions",
  "authors": [
    "Dong Li",
    "Xiaoyi Zhang"
  ],
  "comment": "24 pages, to appear in Transactions AMS",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the work by T. Duyckaerts and F. Merle, they studied the variational structure near the ground state solution $W$ of the energy critical wave equation and classified the solutions with the threshold energy $E(W,0)$ in dimensions $d=3,4,5$. In this paper, we extend the results to all dimensions $d\\ge 6$. The main issue in high dimensions is the non-Lipschitz continuity of the nonlinearity which we get around by making full use of the decay property of $W$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-11-25T01:36:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy critical nonlinear wave equation",
      "high dimensions",
      "energy critical wave equation",
      "ground state solution",
      "main issue"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0911.4745L"
    }
  }
}