{
  "id": "math/0607631",
  "version": "v1",
  "published": "2006-07-25T14:25:56.000Z",
  "updated": "2006-07-25T14:25:56.000Z",
  "title": "Global existence for energy critical waves in 3-D domains",
  "authors": [
    "Nicolas Burq",
    "Gilles Lebeau",
    "Fabrice Planchon"
  ],
  "comment": "15 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove that the defocusing quintic wave equation, with Dirichlet boundary conditions, is globally well posed on $H^1_0(\\Omega) \\times L^2(\\Omega)$ for any smooth (compact) domain $\\Omega \\subset \\mathbb{R}^3$. The main ingredient in the proof is an $L^5$ spectral projector estimate, obtained recently by Smith and Sogge, combined with a precise study of the boundary value problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-07-25T14:25:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "energy critical waves",
      "global existence",
      "dirichlet boundary conditions",
      "defocusing quintic wave equation",
      "spectral projector estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......7631B"
    }
  }
}