{
  "id": "2010.04612",
  "version": "v1",
  "published": "2020-10-09T14:41:06.000Z",
  "updated": "2020-10-09T14:41:06.000Z",
  "title": "Continuity of the data-to-solution map for the FORQ equation in Besov Spaces",
  "authors": [
    "John Holmes",
    "Feride Tiglay",
    "Ryan Thompson"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "For Besov spaces $B^s_{p,r}(\\rr)$ with $s>\\max\\{ 2 + \\frac1p , \\frac52\\} $, $p \\in (1,\\infty]$ and $r \\in [1 , \\infty)$, it is proved that the data-to-solution map for the FORQ equation is not uniformly continuous from $B^s_{p,r}(\\rr)$ to $C([0,T]; B^s_{p,r}(\\rr))$. The proof of non-uniform dependence is based on approximate solutions and the Littlewood-Paley decomposition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T14:41:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "forq equation",
      "data-to-solution map",
      "besov spaces",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}