The properties of solutions to the dissipative 2-component Camassa–Holm system. Issue 6 (2nd June 2016)

• Record Type: Journal Article
• Authors: Ming, Sen; Yang, Han; Chen, Zili; Yong, Ls
• Is Part Of: Applicable analysis. Volume 95:Issue 6(2016)
• Page Start: 1165
• Page End: 1183
• Publication Date: 2016-06-02
• Subjects: local well-posedness -- dissipative 2-component Camassa–Holm system -- blow-up -- global solution -- infinite propagation speed; 35G25 -- 35L15 -- 35Q58; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1055557
• Languages: English
• ISSNs: 0003-6811

Abstract

Abstract : The local well-posedness for the Cauchy problem of the dissipative 2-component Camassa–Holm system is established by using the Littlewood–Paley theory and a priori estimates of solutions to the transport equation. The blow-up results, the exact blow-up rate, and the global existence of solutions to the system are analyzed. Moreover, the infinite propagation speed of solutions is investigated. The novelty in this paper is that the effects of the diffusion coefficient and dissipative coefficient to the solutions are given in an apparent form.