Wave breaking for the Kakutani-Matsuuchi model

TL;DR

This paper demonstrates wave breaking in the Kakutani-Matsuuchi model, where water wave surface elevation remains bounded while the slope becomes unbounded in finite time under certain initial conditions.

Contribution

The paper proves wave breaking phenomena for the Kakutani-Matsuuchi model, highlighting the conditions under which the slope becomes unbounded while the surface elevation stays bounded.

Findings

Wave breaking occurs in the model with sufficiently negative initial slope.

The surface elevation remains bounded during wave breaking.

Slope becomes unbounded in finite time.

Abstract

In this paper, we consider the Kakutani-Matsuuchi model which describes the surface elevation of the water-waves under the effect of viscosity. We show wave breaking for the Kakutani-Matsuuchi model, namely, the solution remains bounded but its slope becomes unbounded in finite time, the slope of the initial data is sufficiently negative.