On the wave-breaking phenomena for the periodic two-component Dullin–Gottwald–Holm system

Considered herein is the well-posedness problem of the periodic two-component Dullin–Gottwald–Holm (DGH) system on the circle, which can be derived from Eulerʼs equation with constant vorticity in shallow water waves moving over a linear shear flow. The result of blow-up solutions for certain initial profiles in a manner which corresponds to wave-breaking is established.