Blow-up phenomena and local well-posedness for a generalized Camassa–Holm equation with cubic nonlinearity. (March 2017)

• Record Type: Journal Article
• Authors: Li, Min; Yin, Zhaoyang
• Is Part Of: Nonlinear analysis. Volume 151(2017)
• Page Start: 208
• Page End: 226
• Publication Date: 2017-03
• Subjects: A generalized Camassa–Holm equation with cubic nonlinearity -- Local well-posedness -- Blow-up criterion -- 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.2016.12.003
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper we consider the Cauchy problem for a generalized Camassa–Holm equation with cubic nonlinearity in Besov spaces. We first establish the local well-posedness of the equation in the Besov space B p, r s by using the Littlewood–Paley theory. Then, under a sign condition we reach the sign-preserved property and a precise blow-up criterion. Applying this precise criterion we present a blow-up result and the precise blow-up rate for strong solutions to the equation.