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Zbl 1038.76011
Constantin, Adrian; Strauss, Walter
Exact steady periodic water waves with vorticity. (English)
[J] Commun. Pure Appl. Math. 57, No. 4, 481-527 (2004). ISSN 0010-3640

Summary: We consider the classical water wave problem described by Euler equations with a free surface under the influence of gravity over a flat bottom. We construct two-dimensional inviscid periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use bifurcation and degree theory to construct a global connected set of such solutions.

MSC 2000:: *76B15 Wave motions (fluid mechanics)
35Q35 Other equations arising in fluid mechanics

Keywords: Euler equations; free surface; gravity; flat bottom; two-dimensional inviscid periodic traveling waves; symmetric waves; bifurcation; degree theory; global connected solutions; uniform regularity

Cited in: Zbl 1067.76014 Zbl 1075.34004

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