Revisit to wave breaking phenomena for the periodic Dullin–Gottwald–Holm equation

Abstract

In this paper, we mainly devote to investigate the periodic Dullin–Gottwald–Holm equation. By overcoming the difficulties caused by the complicated mixed nonlinear structure, a very useful priori estimate is derived in Lemma 2.7. Based on Hα1-conservation and L∞-estimate of solution, some new blow-up phenomena are derived for the periodic Dullin–Gottwald–Holm equation under different initial conditions.