Well-posedness and persistence property for a shallow water wave equation for waves of large amplitude

ABSTRACT

In this paper, we study the local well-posedness for a shallow water wave equation for waves of large amplitude in the framework of Sobolev spaces. By using Kato’s semigroup approach for quasilinear evolution equations, we establish the local well-posedness in $H^s$ with $s>\frac{3}{2}$. Furthermore, we show a persistence property for strong solutions.

KEYWORDS:

• Shallow water wave equation
• local well-posedness
• persistence property

AMS SUBJECT CLASSIFICATIONS:

• 35A01
• 35G25
• 35Q53

Acknowledgements

This work is supported by the Graduate Student Science and Technology Innovation Activities of Beijing Institute of Technology (NO.2017CX10058).

Disclosure statement

No potential conflict of interest was reported by the authors.