{"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 $0\\leq r<s$. Finally, th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.07996","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}