Advanced

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
language
English
LU publication?
yes
id
95066c56-c01f-40bc-9af4-8a690aba3fd2 (old id 4450994)
date added to LUP
2014-06-19 14:19:11
date last changed
2017-11-05 03:02:03
@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},
  keyword      = {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          = {http://dx.doi.org/10.1017/jfm.2014.131},
  volume       = {746},
  year         = {2014},
}