The well-posedness, blow-up, and traveling waves for a two-component Fornberg–Whitham system

Abstract

In this paper, the two-component Fornberg–Whitham system is studied. We first investigate the local well-posedness in classical Sobolev space and establish a blow-up criterion by a local-in-time priori estimate, and then, we give some sufficient conditions on the initial data to lead to wave breaking. Finally, we discuss analytically the existence of periodic traveling waves by the bifurcation theorem.