Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity
(2015) In Proceedings of the Royal Society of Edinburgh. Section A 145(4). p.791-883- Abstract
- We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy H subject to the constraint I = 2 mu, where I is the wave momentum and 0 < mu << 1. Since H and I are both conserved quantities, a standard argument asserts the stability of the set D-mu of minimizers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-de Vries... (More)
- We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy H subject to the constraint I = 2 mu, where I is the wave momentum and 0 < mu << 1. Since H and I are both conserved quantities, a standard argument asserts the stability of the set D-mu of minimizers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrodinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as mu down arrow 0. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7767751
- author
- Groves, M. D. and Wahlén, Erik LU
- organization
- publishing date
- 2015
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- water waves, solitary waves, vorticity, calculus of variations
- in
- Proceedings of the Royal Society of Edinburgh. Section A
- volume
- 145
- issue
- 4
- pages
- 791 - 883
- publisher
- Royal Society of Edinburgh
- external identifiers
-
- wos:000358440200008
- scopus:84946185786
- ISSN
- 0308-2105
- DOI
- 10.1017/S0308210515000116
- project
- Nonlinear Water Waves
- language
- English
- LU publication?
- yes
- id
- 9ce6fc9c-51b7-4326-9b9d-1afcc260ee48 (old id 7767751)
- date added to LUP
- 2016-04-01 14:38:49
- date last changed
- 2022-03-14 06:59:38
@article{9ce6fc9c-51b7-4326-9b9d-1afcc260ee48,
abstract = {{We present an existence and stability theory for gravity-capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy H subject to the constraint I = 2 mu, where I is the wave momentum and 0 < mu << 1. Since H and I are both conserved quantities, a standard argument asserts the stability of the set D-mu of minimizers: solutions starting near D-mu remain close to D-mu in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg-de Vries equation (for strong surface tension) or a nonlinear Schrodinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as mu down arrow 0.}},
author = {{Groves, M. D. and Wahlén, Erik}},
issn = {{0308-2105}},
keywords = {{water waves; solitary waves; vorticity; calculus of variations}},
language = {{eng}},
number = {{4}},
pages = {{791--883}},
publisher = {{Royal Society of Edinburgh}},
series = {{Proceedings of the Royal Society of Edinburgh. Section A}},
title = {{Existence and conditional energetic stability of solitary gravity-capillary water waves with constant vorticity}},
url = {{https://lup.lub.lu.se/search/files/4085338/7990424.pdf}},
doi = {{10.1017/S0308210515000116}},
volume = {{145}},
year = {{2015}},
}