Steady periodic capillary-gravity waves with vorticity
Författare
Summary, in English
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.
Avdelning/ar
- Matematik (naturvetenskapliga fakulteten)
- Partial differential equations
Publiceringsår
2006
Språk
Engelska
Sidor
921-943
Publikation/Tidskrift/Serie
SIAM Journal on Mathematical Analysis
Volym
38
Issue
3
Dokumenttyp
Artikel i tidskrift
Förlag
Society for Industrial and Applied Mathematics
Ämne
- Mathematics
Nyckelord
- capillarity
- bifurcation theory
- water waves
- vorticity
Status
Published
Forskningsgrupp
- Partial differential equations
ISBN/ISSN/Övrigt
- ISSN: 0036-1410