{
  "id": "2202.06304",
  "version": "v1",
  "published": "2022-02-13T12:59:17.000Z",
  "updated": "2022-02-13T12:59:17.000Z",
  "title": "Ill_posedness for a two_component Novikov system in Besov space",
  "authors": [
    "Xing Wu",
    "Min Li"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the Cauchy problem for a two-component Novikov system on the line. By specially constructed initial data $(\\rho_0, u_0)$ in $B_{p, \\infty}^{s-1}(\\mathbb{R})\\times B_{p, \\infty}^s(\\mathbb{R})$ with $s>\\max\\{2+\\frac{1}{p}, \\frac{5}{2}\\}$ and $1\\leq p \\leq \\infty$, we show that any energy bounded solution starting from $(\\rho_0, u_0)$ does not converge back to $(\\rho_0, u_0)$ in the metric of $B_{p, \\infty}^{s-1}(\\mathbb{R})\\times B_{p, \\infty}^s(\\mathbb{R})$ as time goes to zero, thus results in discontinuity of the data-to-solution map and ill-posedness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-13T12:59:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "besov space",
      "two-component novikov system",
      "specially constructed initial data",
      "cauchy problem",
      "data-to-solution map"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}