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

TL;DR

This paper analyzes a two-component Fornberg-Whitham system, establishing well-posedness, conditions for wave breaking, and proving the existence of periodic travelling waves.

Contribution

It provides new results on the well-posedness, blow-up scenarios, and existence of travelling waves for the two-component Fornberg-Whitham system.

Findings

Well-posedness in Sobolev spaces established.

Conditions for wave breaking identified.

Existence of periodic travelling waves proven.

Abstract

In this paper, the two-component Fornberg-Whitham system is studied. We firstly investigate the well-posedness in classical Sobolev Space and show a blow-up scenario by local-in-time a priori estimates, then we present some sufficient conditions on the initial data to lead to wave breaking. Furthermore, we establish analytically the existence of periodic travelling waves.