A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation

Kenta Ohi, Tatsuo Iguchi

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

The Benjamin-Ono equation is known as a model of internal long waves in stratified fluids or two-fluid systems. In this paper, we consider the validity of this type of modeling of a two-phase problem for capillary-gravity waves, which is a free boundary problem for the incompressible Euler equation with the irrotational condition. We show that the solutions of the free boundary problem split up into two waves and the shape of each wave is governed by the Benjamin-Ono equation in a slow time scale.

Original languageEnglish
Pages (from-to)1205-1240
Number of pages36
JournalDiscrete and Continuous Dynamical Systems
Volume23
Issue number4
DOIs
Publication statusPublished - 2009 Apr 1

Keywords

  • Benjamin-Ono equation
  • Internal waves
  • Two-phase problem

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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