Continuity properties of the data-to-solution map for the two-component higher order Camassa–Holm system. (February 2019)

• Record Type: Journal Article
• Authors: Wang, Feng; Li, Fengquan
• Is Part Of: Nonlinear analysis. Volume 45(2019)
• Page Start: 866
• Page End: 876
• Publication Date: 2019-02
• Subjects: Two-component higher order Camassa–Holm system -- Cauchy problem -- Well-posedness -- Hölder continuity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2018.08.008
• Languages: English
• ISSNs: 1468-1218

Abstract

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 .