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

Abstract

Considered herein is the well-posedness problem of the two-component Dullin–Gottwald–Holm system, which can be derived from the Euler equation with constant vorticity in shallow water waves moving over a linear shear flow. It is shown that the solutions to this system have singularities that correspond to wave breaking. Moreover, two sufficient conditions to guarantee wave-breaking phenomena are given. Finally, a result of global solutions is formulated.