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

Kenta Ohi; Tatsuo Iguchi

doi:10.3934/dcds.2009.23.1205

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

Kenta Ohi, Tatsuo Iguchi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	1205-1240
Number of pages	36
Journal	Discrete and Continuous Dynamical Systems
Volume	23
Issue number	4
DOIs	https://doi.org/10.3934/dcds.2009.23.1205
Publication status	Published - 2009 Apr

Keywords

Benjamin-Ono equation
Internal waves
Two-phase problem

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/dcds.2009.23.1205

Fingerprint Dive into the research topics of 'A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation'. Together they form a unique fingerprint.

Cite this

@article{01a1cc05fe684ce9bd89f3f067eb7496,

title = "A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation",

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.",

keywords = "Benjamin-Ono equation, Internal waves, Two-phase problem",

author = "Kenta Ohi and Tatsuo Iguchi",

year = "2009",

month = apr,

doi = "10.3934/dcds.2009.23.1205",

language = "English",

volume = "23",

pages = "1205--1240",

journal = "Discrete and Continuous Dynamical Systems",

issn = "1078-0947",

publisher = "Southwest Missouri State University",

number = "4",

}

TY - JOUR

T1 - A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation

AU - Ohi, Kenta

AU - Iguchi, Tatsuo

PY - 2009/4

Y1 - 2009/4

N2 - 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.

AB - 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.

KW - Benjamin-Ono equation

KW - Internal waves

KW - Two-phase problem

UR - http://www.scopus.com/inward/record.url?scp=62649143819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=62649143819&partnerID=8YFLogxK

U2 - 10.3934/dcds.2009.23.1205

DO - 10.3934/dcds.2009.23.1205

M3 - Article

AN - SCOPUS:62649143819

VL - 23

SP - 1205

EP - 1240

JO - Discrete and Continuous Dynamical Systems

JF - Discrete and Continuous Dynamical Systems

SN - 1078-0947

IS - 4

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this