### 抄録

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.

元の言語 | English |
---|---|

ページ（範囲） | 1205-1240 |

ページ数 | 36 |

ジャーナル | Discrete and Continuous Dynamical Systems |

巻 | 23 |

発行部数 | 4 |

DOI | |

出版物ステータス | Published - 2009 4 |

### Fingerprint

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Analysis

### これを引用

**A two-phase problem for capillary-gravity waves and the Benjamin-Ono equation.** / Ohi, Kenta; Iguchi, Tatsuo.

研究成果: Article

*Discrete and Continuous Dynamical Systems*, 巻. 23, 番号 4, pp. 1205-1240. https://doi.org/10.3934/dcds.2009.23.1205

}

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 -