{
  "id": "1909.03556",
  "version": "v1",
  "published": "2019-09-08T22:23:22.000Z",
  "updated": "2019-09-08T22:23:22.000Z",
  "title": "A remark on norm inflation for nonlinear wave equations",
  "authors": [
    "Justin Forlano",
    "Mamoru Okamoto"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this note, we study the ill-posedness of nonlinear wave equations (NLW). Namely, we show that NLW experiences norm inflation at every initial data in negative Sobolev spaces. This result covers a gap left open in a paper of Christ, Colliander, and Tao (2003) and extends the result by Oh, Tzvetkov, and the second author (2019) to non-cubic integer nonlinearities. In particular, for some low dimensional cases, we obtain norm inflation above the scaling critical regularity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-08T22:23:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35L05",
      "35B30"
    ],
    "keywords": [
      "nonlinear wave equations",
      "nlw experiences norm inflation",
      "low dimensional cases",
      "gap left open",
      "non-cubic integer nonlinearities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}