Symmetry of steady periodic water waves with vorticity

Research output: Contribution to journalArticlepeer-review


The symmetry and monotonicity properties of steady periodic gravity water waves are established for arbitrary vorticities if the wave profile is monotone near the trough and every streamline attains a minimum below the trough. The proof uses the method of moving planes.

Original languageEnglish (US)
Pages (from-to)2203-2214
Number of pages12
JournalPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number1858
StatePublished - Sep 15 2007
Externally publishedYes


  • Maximum principles
  • Nonlinear elliptic
  • Symmetry
  • Vorticity
  • Water waves

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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