{
  "id": "1504.05652",
  "version": "v1",
  "published": "2015-04-22T04:42:09.000Z",
  "updated": "2015-04-22T04:42:09.000Z",
  "title": "Long time existence for semilinear wave equations on asymptotically flat space-times",
  "authors": [
    "Chengbo Wang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the long time existence of solutions to some semilinear wave equations of the form $\\Box u=|u|^p$ with compactly supported small data, on a large class of (1+n)-dimensional nonstationary asymptotically flat backgrounds, which models the black hole space-times. Under the assumption that uniform energy bounds and a weak form of local energy estimates hold forward in time, we give a lower bound of the lifespan when n=3 and p is less than the critical one, which is sharp in general. For the critical case with n=3, 4, we get an exponential lower bound of the lifespan.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-22T04:42:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35L15",
      "35L70",
      "35B33",
      "83C57",
      "58J45"
    ],
    "keywords": [
      "long time existence",
      "semilinear wave equations",
      "asymptotically flat space-times",
      "energy estimates hold forward",
      "local energy estimates hold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150405652W"
    }
  }
}