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

Presented by: 
Tatsuo Iguchi Keio University
Date: 
Wednesday 9th August 2017 - 09:00 to 10:00
Venue: 
INI Seminar Room 1
Abstract: 
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 $\delta^2$, 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 $\delta^4$. 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 $\delta^6$.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons