{
  "id": "2209.07865",
  "version": "v1",
  "published": "2022-09-16T11:39:10.000Z",
  "updated": "2022-09-16T11:39:10.000Z",
  "title": "Norm inflation and ill-posedness for the Fornberg-Whitham equation",
  "authors": [
    "Jinlu Li",
    "Xing Wu",
    "Yanghai Yu",
    "Weipeng Zhu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove that the Cauchy problem for the Fornberg-Whitham equation is not locally well-posed in $B^s_{p,r}(\\R)$ with $(s,p,r)\\in (1,1+\\frac1p)\\times[2,\\infty)\\times [1,\\infty]$ or $(s,p,r)\\in \\{1\\}\\times[2,\\infty)\\times [1,2]$ by showing norm inflation phenomena of the solution for some special initial data.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-09-16T11:39:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fornberg-whitham equation",
      "ill-posedness",
      "special initial data",
      "showing norm inflation phenomena",
      "cauchy problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}