Isobe-Kakinuma model for water waves as a higher order shallow water approximation

NWWW01 - Nonlinear water waves

We justify rigorously an Isobe-Kakinuma model for water waves as a higher order shallow water approximation in the case of a flat bottom. It is known that the full water wave equations are approximated by the shallow water equations with an error of order $\delta2$, where $\delta$ is a small nondimensional parameter defined as the ratio of the typical wavelength to the mean depth. The Green-Naghdi equations are known as higher order approximate equations to the water wave equations with an error of order $\delta4$. In this paper we show that the Isobe-Kakinuma model is a much higher approximation to the water wave equations with an error of order $\delta^6$.

This talk is part of the Isaac Newton Institute Seminar Series series.