Blow-up phenomena for the weakly dissipative Dullin-Gottwald-Holm equation revisited

Abstract

In this paper, we investigate the Cauchy problem for the weakly dissipative Dullin-Gottwald-Holm equation. We first establish the local well-posedness result by Kato’s semigroup theory. Then, we obtain the precise blow-up scenario and present some blow-up results for strong solutions to the equation. Finally, we discuss the blow-up rate of the wave-breaking solutions. This result complements the early one in the literature, such as Novruzov [J. Math. Phys. 54, 092703 (2013)].