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Non-existence of three-dimensional travelling water waves with constant non-zero vorticity

Wahlén, Erik LU (2014) In Journal of Fluid Mechanics 746. p.2-2
Abstract
We prove that there are no three-dimensional bounded travelling gravity waves with constant non-zero vorticity on water of finite depth. The result also holds for gravity–capillary waves under a certain condition on the pressure at the surface, which is satisfied by sufficiently small waves. The proof relies on unique continuation arguments and Liouville-type results for elliptic equations.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
mathematical foundations, waves/free-surface flows
in
Journal of Fluid Mechanics
volume
746
pages
2 - 2
publisher
Cambridge University Press
external identifiers
  • wos:000335384200002
  • scopus:84930208402
ISSN
0022-1120
DOI
10.1017/jfm.2014.131
project
Nonlinear Water Waves
language
English
LU publication?
yes
id
95066c56-c01f-40bc-9af4-8a690aba3fd2 (old id 4450994)
date added to LUP
2016-04-01 09:53:57
date last changed
2022-02-09 20:42:41
@article{95066c56-c01f-40bc-9af4-8a690aba3fd2,
  abstract     = {{We prove that there are no three-dimensional bounded travelling gravity waves with constant non-zero vorticity on water of finite depth. The result also holds for gravity–capillary waves under a certain condition on the pressure at the surface, which is satisfied by sufficiently small waves. The proof relies on unique continuation arguments and Liouville-type results for elliptic equations.}},
  author       = {{Wahlén, Erik}},
  issn         = {{0022-1120}},
  keywords     = {{mathematical foundations; waves/free-surface flows}},
  language     = {{eng}},
  pages        = {{2--2}},
  publisher    = {{Cambridge University Press}},
  series       = {{Journal of Fluid Mechanics}},
  title        = {{Non-existence of three-dimensional travelling water waves with constant non-zero vorticity}},
  url          = {{https://lup.lub.lu.se/search/files/1369033/4451002.pdf}},
  doi          = {{10.1017/jfm.2014.131}},
  volume       = {{746}},
  year         = {{2014}},
}