Well-posedness, global existence and blow-up phenomena for an integrable multi-component Camassa–Holm system. (September 2016)

• Record Type: Journal Article
• Authors: Zhang, Zeng; Yin, Zhaoyang
• Is Part Of: Nonlinear analysis. Volume 142(2016)
• Page Start: 112
• Page End: 133
• Publication Date: 2016-09
• Subjects: 35G25 -- 35L05; Integrable multi-component Camassa–Holm system -- Local well-posedness -- Global existence -- Blow-up; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2016.04.004
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is concerned with a new integrable multi-component Camassa–Holm system, which has been proven to be integrable and has peakon solutions. This system includes many one-component and two-component Camassa–Holm type systems as special cases. In this paper, we first establish the local well-posedness and a continuation criterion for the system, then we present several global existence and blow-up results for two important integrable two-component subsystems. Our obtained results cover and improve considerably recent results in Gui et al. (2013), Yan et al. (2015).