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Steady periodic capillary-gravity waves with vorticity

På svenska

Author

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.

Department/s

Publishing year

2006

Language

English

Pages

921-943

Publication/Series

SIAM Journal on Mathematical Analysis

Volume

38

Issue

3

Document type

Journal article

Publisher

Society for Industrial and Applied Mathematics

Topic

  • Mathematics

Keywords

  • capillarity
  • bifurcation theory
  • water waves
  • vorticity

Status

Published

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0036-1410