{
  "id": "2011.14125",
  "version": "v1",
  "published": "2020-11-28T12:38:37.000Z",
  "updated": "2020-11-28T12:38:37.000Z",
  "title": "Non-uniform dependence on initial data for the 2D viscous shallow water equations",
  "authors": [
    "Jinlu Li",
    "Yanghai Yu",
    "Weipeng Zhu"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "The failure of uniform dependence on the data is an interesting property of classical solution for a hyperbolic system. In this paper, we consider the solution map of the Cauchy problem to the 2D viscous shallow water equations which is a hyperbolic-parabolic system. We prove that the solution map of this problem is not uniformly continuous in Sobolev spaces $H^s\\times H^{s}$ for $s>2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-28T12:38:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q35",
      "35A01",
      "76N10"
    ],
    "keywords": [
      "2d viscous shallow water equations",
      "initial data",
      "non-uniform dependence",
      "solution map",
      "hyperbolic system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}