{
  "id": "1905.13739",
  "version": "v1",
  "published": "2019-05-31T17:44:40.000Z",
  "updated": "2019-05-31T17:44:40.000Z",
  "title": "Threshold for blowup for the supercritical cubic wave equation",
  "authors": [
    "Irfan Glogić",
    "Maciej Maliborski",
    "Birgit Schörkhuber"
  ],
  "comment": "17 pages, 4 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we discuss singularity formation for the focusing cubic wave equation in the energy supercritical regime. For this equation an $\\textit{explicit}$ nontrivial self-similar blowup solution was recently found by the first and third author in \\cite{GlogicSchoerkhuber}. In the seven dimensional case it was proven to be stable along a co-dimension one manifold of initial data. Here, we provide numerical evidence that this solution is in fact a critical solution at the threshold between finite-time blowup and dispersion. Furthermore, we discuss the spectral problem arising in the stability analysis in general dimensions $d \\geq 5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-31T17:44:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supercritical cubic wave equation",
      "nontrivial self-similar blowup solution",
      "focusing cubic wave equation",
      "seven dimensional case",
      "singularity formation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}