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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1704.02419 |
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Table of Contents:
- 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 $O(δ^2)$, where $δ$ is a small nondimensional parameter defined as the ratio of the mean depth to the typical wavelength. The Green-Naghdi equations are known as higher order approximate equations to the water wave equations with an error of order $O(δ^4)$. In this paper we show that the Isobe-Kakinuma model is a much higher order approximation to the water wave equations with an error of order $O(δ^6)$.