Continuity properties of the data-to-solution map for the two-component higher order Camassa–Holm system. (February 2019) - Wang, Feng; Li, Fengquan
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 ( R ) × H s − 2 ( R ), s > 7 2 and its solution map is continuous. We show that the solution map is Hölder continuous in H s ( R ) × H s − 2 ( R ) equipped with the H r ( R ) × H r − 2 ( R ) -topology for 1 ≤ r < s, and the Hölder exponent is expressed in terms of s and r .