A long wave approximation for capillary-gravity waves and an effect of the bottom

研究成果: Article査読

20 被引用数 (Scopus)

抄録

The Korteweg-de Vries (KdV) equation is known as a model of long waves in an infinitely long canal over a flat bottom and approximates the 2-dimensional water wave problem, which is a free boundary problem for the incompressible Euler equation with the irrotational condition. In this article, we consider the validity of this approximation in the case of the presence of the surface tension. Moreover, we consider the case where the bottom is not flat and study an effect of the bottom to the long wave approximation. We derive a system of coupled KdV like equations and prove that the dynamics of the full problem can be described approximately by the solution of the coupled equations for a long time interval. We also prove that if the initial data and the bottom decay at infinity in a suitable sense, then the KdV equation takes the place of the coupled equations.

本文言語English
ページ(範囲)37-85
ページ数49
ジャーナルCommunications in Partial Differential Equations
32
1
DOI
出版ステータスPublished - 2007 1

ASJC Scopus subject areas

  • 分析
  • 応用数学

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