{
  "id": "1810.07681",
  "version": "v1",
  "published": "2018-10-17T17:38:58.000Z",
  "updated": "2018-10-17T17:38:58.000Z",
  "title": "Co-dimension one stable blowup for the supercritical cubic wave equation",
  "authors": [
    "Irfan Glogić",
    "Birgit Schörkhuber"
  ],
  "comment": "47 pages",
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP"
  ],
  "abstract": "For the focusing cubic wave equation, we find an explicit, non-trivial self-similar blowup solution $u^*_T$, which is defined on the whole space and exists in all supercritical dimensions $d \\geq 5$. For $d=7$, we analyze its stability properties without any symmetry assumptions and prove the existence of a co-dimension one Lipschitz manifold consisting of initial data whose solutions blowup in finite time and converge asymptotically to $u^*_T$ (modulo space-time shifts and Lorentz boosts) in the backward lightcone of the blowup point. The underlying topology is strictly above scaling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-17T17:38:58.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supercritical cubic wave equation",
      "stable blowup",
      "co-dimension",
      "non-trivial self-similar blowup solution",
      "focusing cubic wave equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 47,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}