{
  "id": "1712.07996",
  "version": "v1",
  "published": "2017-12-21T15:11:31.000Z",
  "updated": "2017-12-21T15:11:31.000Z",
  "title": "Well-posedness and peakons for a higher-order $μ$-Camassa-Holm equation",
  "authors": [
    "Feng Wang",
    "Fengquan Li",
    "Zhijun Qiao"
  ],
  "comment": "26 pages",
  "categories": [
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper, we study the Cauchy problem of a higher-order $\\mu$-Camassa-Holm equation. By employing the Green's function of $(\\mu+\\partial_{x}^{4})^{-1}$, we obtain the explicit formula of the inverse function $(\\mu+\\partial_{x}^{4})^{-1}w$ and local well-posedness for the equation in Sobolev spaces $H^{s}(\\mathbb{S})$, $s>\\frac{7}{2}$. Then we prove the existence of global strong solutions and weak solutions. Moreover, we show that the solution map is H\\\"{o}lder continuous in $H^{s}(\\mathbb{S})$, $s\\geq 4$, equipped with the $H^{r}(\\mathbb{S})$-topology for $0\\leq r<s$. Finally, the equation is shown to admit single peakon solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-21T15:11:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35G25",
      "35L05",
      "35B30"
    ],
    "keywords": [
      "camassa-holm equation",
      "higher-order",
      "admit single peakon solutions",
      "global strong solutions",
      "greens function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}