{"paper":{"title":"On the Cauchy problem 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":"2017-12-27T13:46:23Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09583","kind":"arxiv","version":1},"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"}