The local well-posedness, blow-up criteria and Gevrey regularity of solutions for a two-component high-order Camassa–Holm system. (June 2017)

• Record Type: Journal Article
• Authors: Zhang, Lei; Li, Xiuting
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 414
• Page End: 440
• Publication Date: 2017-06
• Subjects: Local well-posedness -- Besov spaces -- Blow-up -- Gevrey regularity -- Analyticity; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.12.001
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper studies the Cauchy problem for a two-component high-order Camassa–Holm system proposed in Escher and Lyons (2015). First, we investigate the local well-posedness of the system in the Besov spaces B p, r s × B p, r s − 2 with s > max { 3 + 1 p, 7 2, 4 − 1 p } and p, r ∈ [ 1, ∞ ] . Second, by means of the Littlewood–Paley decomposition technique and the conservative property at hand, we derive a blow-up criteria for the strong solution. Finally, we study the Gevrey regularity and analyticity of the solutions to the system in the Gevrey–Sobolev spaces. In particular, we get a lower bound of the lifespan and the continuity of the data-to-solution mapping.