Stokeswaves with vorticity |
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Authors: | Vera Mikyoung Hur |
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Institution: | (2) Department of Mathematics, University of Texas – Pan American, Edinburg, USA; |
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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. |
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Keywords: | |
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