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

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.

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Cited by in corpus (3)

• Well-posedness of the two-component Fornberg-Whitham system in Besov spaces
• Continuity properties of the data-to-solution map and ill-posedness for a two-component Fornberg-Whitham system
• Non-uniform dependence on periodic initial data for the two-component Fornberg-Whitham system in Besov spaces