Global existence and blow-up phenomena for a weakly dissipative periodic 2-component Camassa-Holm system

Abstract

We first establish local well posedness for a weakly dissipative periodic 2-component Camassa-Holm system. We then present two global existence results for strong solutions to the equation. We finally obtain several blow-up results and the blow-up rate of strong solutions to the equation.

Blow-Up for a Periodic Two-Component Camassa-Holm Equation with Generalized Weakly Dissipation

“…Hu and Yin [11] study the blow-up of solutions to a weakly dissipative periodic rod equation. Hu considered global existence and blow-up phenomena for a weakly dissipative two-component Camassa-Holm system [12] [13]. The purpose of this paper is to study the blow-up phenomenon of the solutions of Equation (1.1).…”

Global existence and propagation speed for a generalized Camassa–Holm model with both dissipation and dispersion

“…Hu and Yin discussed the blow-up and blow-up rate of solutions to a weakly dissipative periodic rod equation [18]. Later, Hu studied the global existence and blow-up phenomena for a weakly dissipative periodic 2-component Camassa-Holm system [19]. In 2014, Zhou, Mu and Wang [54] considered the weakly dissipative gCH equation (i.e.…”

The Cauchy Problem for a Dissipative Periodic 2-Component Degasperis-Procesi System

“…Recently, a large amount of literature was devoted to the 2component Camassa-Holm system [30][31][32][33][34][35][36][37][38][39]. For example, Hu [40]…”

“…Motivated by the work in [20,28,32,[40][41][42][43], we study the dissipative periodic 2-component Degasperis-Procesi system (1). We note that the Cauchy problem of system (1) in Besov space has not been discussed yet.…”