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Steady periodic capillary-gravity waves with vorticity

Wahlén, Erik LU (2006) In SIAM Journal on Mathematical Analysis 38(3). p.921-943
Abstract
In this paper we prove the existence of steady periodic two-dimensional capillary-gravity waves on flows with an arbitrary vorticity distribution. The original free-surface problem is first transformed to a second-order quasi-linear elliptic equation with a second-order quasi-linear boundary condition in a fixed domain by a change of variables. We then use local bifurcation theory combined with the Schauder theory of elliptic equations with Venttsel boundary conditions and spectral theory in Pontryagin spaces to construct the solutions. We show that some bifurcation points are simple while others are double, a situation already known to occur in the case of irrotational capillary-gravity waves.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
capillarity, bifurcation theory, water waves, vorticity
in
SIAM Journal on Mathematical Analysis
volume
38
issue
3
pages
921 - 943
publisher
SIAM
external identifiers
  • wos:000242572500012
  • scopus:33947375479
ISSN
0036-1410
DOI
10.1137/050630465
language
English
LU publication?
yes
id
c9d49095-6b0b-4ec9-a0e9-c90e1f8f13da (old id 637731)
date added to LUP
2007-12-10 12:18:56
date last changed
2018-09-16 03:40:43
@article{c9d49095-6b0b-4ec9-a0e9-c90e1f8f13da,
  abstract     = {In this paper we prove the existence of steady periodic two-dimensional capillary-gravity waves on flows with an arbitrary vorticity distribution. The original free-surface problem is first transformed to a second-order quasi-linear elliptic equation with a second-order quasi-linear boundary condition in a fixed domain by a change of variables. We then use local bifurcation theory combined with the Schauder theory of elliptic equations with Venttsel boundary conditions and spectral theory in Pontryagin spaces to construct the solutions. We show that some bifurcation points are simple while others are double, a situation already known to occur in the case of irrotational capillary-gravity waves.},
  author       = {Wahlén, Erik},
  issn         = {0036-1410},
  keyword      = {capillarity,bifurcation theory,water waves,vorticity},
  language     = {eng},
  number       = {3},
  pages        = {921--943},
  publisher    = {SIAM},
  series       = {SIAM Journal on Mathematical Analysis},
  title        = {Steady periodic capillary-gravity waves with vorticity},
  url          = {http://dx.doi.org/10.1137/050630465},
  volume       = {38},
  year         = {2006},
}