{
  "id": "1712.09583",
  "version": "v1",
  "published": "2017-12-27T13:46:23.000Z",
  "updated": "2017-12-27T13:46:23.000Z",
  "title": "On the Cauchy problem for a higher-order $μ$-Camassa-Holm equation",
  "authors": [
    "Feng Wang",
    "Fengquan Li",
    "Zhijun Qiao"
  ],
  "comment": "27 pages. arXiv admin note: substantial text overlap with arXiv:1712.07996",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we study the Cauchy problem of a higher-order $\\mu$-Camassa-Holm equation. We first establish the Green's function of $(\\mu-\\partial_{x}^{2}+\\partial_{x}^{4})^{-1}$ and local well-posedness for the equation in Sobolev spaces $H^{s}(\\mathbb{S})$, $s>\\frac{7}{2}$. Then we provide the global existence results for strong solutions and weak solutions. Moreover, we show that the solution map is non-uniformly continuous in $H^{s}(\\mathbb{S})$, $s\\geq 4$. Finally, we prove that the equation admits single peakon solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-27T13:46:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35G25",
      "35L05",
      "35B30"
    ],
    "keywords": [
      "cauchy problem",
      "camassa-holm equation",
      "higher-order",
      "equation admits single peakon solutions",
      "global existence results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}