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Non-existence of three-dimensional travelling water waves with constant non-zero vorticity

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Author

Summary, in English

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.

Department/s

Publishing year

2014

Language

English

Pages

2-2

Publication/Series

Journal of Fluid Mechanics

Volume

746

Document type

Journal article

Publisher

Cambridge University Press

Topic

  • Mathematics

Keywords

  • mathematical foundations
  • waves/free-surface flows

Status

Published

Project

  • Nonlinear Water Waves

Research group

  • Partial differential equations

ISBN/ISSN/Other

  • ISSN: 0022-1120