Global wellposedness of cubic Camassa–Holm equations. (March 2016)

• Record Type: Journal Article
• Authors: Zhang, Qingtian
• Is Part Of: Nonlinear analysis. Volume 133(2016)
• Page Start: 61
• Page End: 73
• Publication Date: 2016-03
• Subjects: Camassa–Holm equations -- Well-posedness -- Kružhikov's theory; 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.2015.11.020
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we study the Cauchy problem of cubic Camassa–Holm equation. This equation is derived from a model of shallow water dynamics. We prove the global existence of entropy weak solution to this problem in space H 1 with its derivative in B V . The stability and uniqueness of entropy weak solution are obtained in W 1, 1 .