Persistence properties and blow-up phenomena for a generalized Camassa–Holm equation

Abstract In this paper, we investigate a generalized Camassa–Holm equation. Firstly, establish the persistence properties of strong solutions for equation in weighted spaces $L^{p}_{\phi}=L^{p}(\mathbb{R},\phi ^{p}\,dx)$ L ϕ p = ( R , d x ) . Then present some sufficient conditions blow-up assuming that initial data satisfy certain conditions, which are more precise than those previous work.