{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:4LB5YQCODODBUX54VUT32J7TDA","short_pith_number":"pith:4LB5YQCO","schema_version":"1.0","canonical_sha256":"e2c3dc404e1b861a5fbcad27bd27f31812fa13b097095d3cb49c6619b725e5a3","source":{"kind":"arxiv","id":"1805.06290","version":1},"attestation_state":"computed","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 $1\\leq r\\frac{7}{2}$ 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