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An Existence Theory for Small-Amplitude Doubly Periodic Water Waves with Vorticity

Lokharu, E. LU ; S. Seth, D. LU and Wahlén, E. LU orcid (2020) In Archive for Rational Mechanics and Analysis 238(2). p.607-637
Abstract

We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field, meaning that the vorticity is collinear to the velocity. The existence theory is based on multi-parameter bifurcation theory.

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Archive for Rational Mechanics and Analysis
volume
238
issue
2
pages
31 pages
publisher
Springer
external identifiers
  • scopus:85088141648
ISSN
0003-9527
DOI
10.1007/s00205-020-01550-2
project
Mathematical aspects of three-dimensional water waves with vorticity
language
English
LU publication?
yes
id
01fec12c-ae8d-45b1-89de-d86a2d1b1ca7
date added to LUP
2020-07-30 10:53:34
date last changed
2025-10-14 10:32:06
@article{01fec12c-ae8d-45b1-89de-d86a2d1b1ca7,
  abstract     = {{<p>We prove the existence of three-dimensional steady gravity-capillary waves with vorticity on water of finite depth. The waves are periodic with respect to a given two-dimensional lattice and the relative velocity field is a Beltrami field, meaning that the vorticity is collinear to the velocity. The existence theory is based on multi-parameter bifurcation theory.</p>}},
  author       = {{Lokharu, E. and S. Seth, D. and Wahlén, E.}},
  issn         = {{0003-9527}},
  language     = {{eng}},
  number       = {{2}},
  pages        = {{607--637}},
  publisher    = {{Springer}},
  series       = {{Archive for Rational Mechanics and Analysis}},
  title        = {{An Existence Theory for Small-Amplitude Doubly Periodic Water Waves with Vorticity}},
  url          = {{http://dx.doi.org/10.1007/s00205-020-01550-2}},
  doi          = {{10.1007/s00205-020-01550-2}},
  volume       = {{238}},
  year         = {{2020}},
}