{
  "id": "2104.06408",
  "version": "v1",
  "published": "2021-04-13T08:04:23.000Z",
  "updated": "2021-04-13T08:04:23.000Z",
  "title": "Ill-posedness for the Euler equations in Besov spaces",
  "authors": [
    "Jinlu Li",
    "Yanghai Yu",
    "Weipeng Zhu"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2104.05973",
  "categories": [
    "math.AP"
  ],
  "abstract": "In the paper, we consider the Cauchy problem to the Euler equations in $\\mathbb{R}^d$ with $d\\geq2$. We construct an initial data $u_0\\in B^\\sigma_{p,\\infty}$ showing that the corresponding solution map of the Euler equations starting from $u_0$ is discontinuous at $t = 0$ in the metric of $B^\\sigma_{p,\\infty}$, which implies the ill-posedness for this equation in $B^\\sigma_{p,\\infty}$. We generalize the periodic result of Cheskidov and Shvydkoy \\cite{Cheskidov}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-13T08:04:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "besov spaces",
      "ill-posedness",
      "cauchy problem",
      "corresponding solution map",
      "periodic result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}