A Mathematical Justification of the Isobe–Kakinuma Model for Water Waves with and without Bottom Topography

研究成果: Article査読

2 被引用数 (Scopus)

抄録

We consider the Isobe–Kakinuma model for water waves in both cases of the flat and the variable bottoms. The Isobe–Kakinuma model is a system of Euler–Lagrange equations for an approximate Lagrangian which is derived from Luke’s Lagrangian for water waves by approximating the velocity potential in the Lagrangian appropriately. The Isobe–Kakinuma model consists of (N+ 1) second order and a first order partial differential equations, where N is a nonnegative integer. We justify rigorously the Isobe–Kakinuma model as a higher order shallow water approximation in the strongly nonlinear regime by giving an error estimate between the solutions of the Isobe–Kakinuma model and of the full water wave problem in terms of the small nondimensional parameter δ, which is the ratio of the mean depth to the typical wavelength. It turns out that the error is of order O(δ4 N + 2) in the case of the flat bottom and of order O(δ4 [ N / 2 ] + 2) in the case of variable bottoms.

本文言語English
ページ(範囲)1985-2018
ページ数34
ジャーナルJournal of Mathematical Fluid Mechanics
20
4
DOI
出版ステータスPublished - 2018 12 1

ASJC Scopus subject areas

  • 数理物理学
  • 凝縮系物理学
  • 計算数学
  • 応用数学

フィンガープリント

「A Mathematical Justification of the Isobe–Kakinuma Model for Water Waves with and without Bottom Topography」の研究トピックを掘り下げます。これらがまとまってユニークなフィンガープリントを構成します。

引用スタイル