{"paper":{"title":"Continuity properties of the data-to-solution map for the two-component higher order Camassa-Holm system","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Fengquan Li, Feng Wang","submitted_at":"2018-05-10T13:07:02Z","abstract_excerpt":"This work studies the Cauchy problem of a two-component higher order Camassa-Holm system, which is well-posed in Sobolev spaces $H^{s}(\\mathbb{R})\\times H^{s-2}(\\mathbb{R})$, $s>\\frac{7}{2}$ and its solution map is continuous. We show that the solution map is H\\\"{o}lder continuous in $H^{s}(\\mathbb{R})\\times H^{s-2}(\\mathbb{R})$ equipped with the $H^{r}(\\mathbb{R})\\times H^{r-2}(\\mathbb{R})$-topology for $1\\leq r<s$, and the H\\\"{o}lder exponent is expressed in terms of $s$ and $r$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.06290","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"}