Local well-posedness and wave breaking results for periodic solutions of a shallow water equation for waves of moderate amplitude

TL;DR

This paper investigates the local well-posedness of a shallow water wave equation and demonstrates that wave breaking is the only singularity type, using semigroup theory for quasi-linear equations.

Contribution

It introduces a Kato-based approach to establish local well-posedness for a periodic shallow water wave model and characterizes wave breaking as the sole singularity.

Findings

Wave breaking can occur as the only singularity.

The model is well-posed locally in time.

Wave surging breakers are identified as singularities.

Abstract

We study the local well-posedness of a periodic nonlinear equation for surface waves of moderate amplitude in shallow water. We use an approach due to Kato which is based on semigroup theory for quasi-linear equations. We also show that singularities for the model equation can occur only in the form of wave breaking, in particular surging breakers.