{
  "id": "2106.00540",
  "version": "v1",
  "published": "2021-06-01T14:53:05.000Z",
  "updated": "2021-06-01T14:53:05.000Z",
  "title": "Ill-posedness for the higher dimensional Camassa-Holm equations in Besov spaces",
  "authors": [
    "Min Li",
    "Yingying Guo"
  ],
  "comment": "13 pages. arXiv admin note: text overlap with arXiv:2104.05973 by other authors",
  "categories": [
    "math.AP"
  ],
  "abstract": "In the paper, by constructing a initial data $u_{0}\\in B^{\\sigma}_{p,\\infty}$ with $\\sigma-2>\\max\\{1+\\frac 1 p, \\frac 3 2\\}$, we prove that the corresponding solution to the higher dimensional Camassa-Holm equations starting from $u_{0}$ is discontinuous at $t=0$ in the norm of $B^{\\sigma}_{p,\\infty}$, which implies that the ill-posedness for the higher dimensional Camassa-Holm equations in $B^{\\sigma}_{p,\\infty}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-01T14:53:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A01",
      "35Q35",
      "37K10",
      "35A01",
      "35Q35",
      "37K10"
    ],
    "keywords": [
      "besov spaces",
      "ill-posedness",
      "higher dimensional camassa-holm equations starting",
      "initial data",
      "corresponding solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}