{
  "id": "1606.06886",
  "version": "v1",
  "published": "2016-06-22T10:39:29.000Z",
  "updated": "2016-06-22T10:39:29.000Z",
  "title": "Global Regularity for Supercritical Nonlinear Dissipative Wave Equations in 3D",
  "authors": [
    "Kyouhei Wakasa",
    "Borislav Yordanov"
  ],
  "comment": "13 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The nonlinear wave equation $u_{tt}-\\Delta u +|u_t|^{p-1}u_t=0$ is shown to be globally well-posed in the Sobolev spaces of radially symmetric functions $H^k_{\\rm rad}({\\bf R}^3)\\times H^{k-1}_{\\rm rad}({\\bf R}^3)$ for all $p\\geq 3$ and $k\\geq 3$. Moreover, global $C^\\infty $ solutions are obtained when the initial data are $C_0^\\infty$ and exponent $p$ is an odd integer. The radial symmetry allows a reduction to the one-dimensional case where an important observation of A. Haraux (2009) can be applied, i.e., dissipative nonlinear wave equations contract initial data in $W^{k,q}({\\bf R})\\times W^{k-1,q}({\\bf R})$ for all $k\\in[1,2]$ and $q\\in [1,\\infty]$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-22T10:39:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L70",
      "35A05"
    ],
    "keywords": [
      "supercritical nonlinear dissipative wave equations",
      "global regularity",
      "nonlinear wave equations contract",
      "equations contract initial data",
      "wave equations contract initial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}