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

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Abstract

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.
Original languageEnglish
Pages (from-to)R2
JournalJournal of Fluid Mechanics
Volume746
DOIs
Publication statusPublished - 2014

Subject classification (UKÄ)

  • Mathematics

Keywords

  • mathematical foundations
  • waves/free-surface flows

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