Travelling water waves with compactly supported vorticity

Jalal Shatah, Samuel Walsh, Chongchun Zeng

Research output: Contribution to journalArticlepeer-review


In this paper, we prove the existence of two-dimensional, travelling, capillary-gravity, water waves with compactly supported vorticity. Specifically, we consider the cases where the vorticity is a δ-function (a point vortex), or has small compact support (a vortex patch). Using a global bifurcation theoretic argument, we construct a continuum of finite-amplitude, finite-vorticity solutions for the periodic point vortex problem. For the non-periodic case, with either a vortex point or patch, we prove the existence of a continuum of small-amplitude, small-vorticity solutions.

Original languageEnglish (US)
Pages (from-to)1529-1564
Number of pages36
Issue number6
StatePublished - Jun 2013

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Applied Mathematics


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