Stokeswaves with vorticity

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Abstract

The existence of periodic waves propagating downstream on the surface of a two-dimensional infinitely deep body of water under the force of gravity is established for a general class of vorticities. When reformulated as an elliptic boundary value problem in a fixed semi-infinite cylinder with a parameter, the operator describing the problem is nonlinear and non-Fredholm. A global connected set of nontrivial solutions is obtained via singular theory of bifurcation. The proof combines a generalized degree theory, global bifurcation theory, and Whyburn's lemma in topology with the Schauder theory for elliptic problems and the maximum principle.

Original languageEnglish (US)
Pages (from-to)331-386
Number of pages56
JournalJournal d'Analyse Mathematique
Volume113
Issue number1
DOIs
StatePublished - Jan 2011

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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