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 | |
| Publication status | Published - 2009 Apr |
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Keywords
- Benjamin-Ono equation
- Internal waves
- Two-phase problem
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis
Cite this
A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation. / Ohi, Kenta; Iguchi, Tatsuo.
In: Discrete and Continuous Dynamical Systems, Vol. 23, No. 4, 04.2009, p. 1205-1240.Research output: Contribution to journal › Article
}
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
VL - 23
SP - 1205
EP - 1240
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
SN - 1078-0947
IS - 4
ER -