{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:K5GVHULJBLOX6DXSHXJ6QVMGLG","short_pith_number":"pith:K5GVHULJ","schema_version":"1.0","canonical_sha256":"574d53d1690add7f0ef23dd3e8558659945fbf32a7d9c0680ecaaa13057f7add","source":{"kind":"arxiv","id":"1712.07996","version":2},"attestation_state":"computed","paper":{"title":"Well-posedness and peakons for a higher-order $\\mu$-Camassa-Holm equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Fengquan Li, Feng Wang, Zhijun Qiao","submitted_at":"2017-12-21T15:11:31Z","abstract_excerpt":"In this paper, we study the Cauchy problem of a higher-order $\\mu$-Camassa-Holm equation. By employing the Green's function of $(\\mu-\\partial_{x}^{2})^{-2}$, we obtain the explicit formula of the inverse function $(\\mu-\\partial_{x}^{2})^{-2}w$ 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 data-to-solution map is H\\\"{o}lder continuous in $H^{s}(\\mathbb{S})$, $s\\geq 4$, equipped with the $H^{r}(\\mathbb{S})$-topology for $0\\leq r\\frac{7}{2}$. Then we prove the existence of global strong solutions and weak solutions. Moreover, we show that the data-to-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