Continuity properties of the data-to-solution map for the two-component higher order Camassa-Holm system

Abstract

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 Hölder 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 $1\le r<s$, and the Hölder exponent is expressed in terms of $s$ and $r$.

13 pages. arXiv admin note: text overlap with arXiv:1712.07996