作为高阶浅水近似的Isobe-Kakinuma水波模型
Isobe-Kakinuma model for water waves as a higher order shallow water approximation
AI总结：
本文在平底条件下严格证明了Isobe-Kakinuma模型可作为水波方程的高阶浅水近似，其误差为$O(δ^6)$阶，显著优于浅水方程和Green-Naghdi方程。
摘要：
我们在平底情形下严格证明了Isobe-Kakinuma水波模型作为高阶浅水近似的合理性。已知完整的水波方程可由浅水方程以$O(δ^2)$阶误差逼近，其中$δ$是一个小的无量纲参数，定义为平均水深与典型波长之比。Green-Naghdi方程被认为是水波方程的高阶近似方程，其误差为$O(δ^4)$阶。在本文中，我们证明Isobe-Kakinuma模型是水波方程的更高阶近似，其误差为$O(δ^6)$阶。
英文摘要：
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 $O(δ^6)$.
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