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Bifurcation of gravity-capillary Stokes waves with constant vorticity

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arxiv 2501.14353 v2 pith:UYR6RGVT submitted 2025-01-24 math.AP

T. Barbieri , M. Berti , A. Maspero , M. Mazzucchelli This is my paper · ORCID
classification math.AP
keywords wavesconstantvorticitybifurcationgravity-capillarystokesvalueswater
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We consider the gravity-capillary water waves equations of a 2D fluid with constant vorticity. By employing variational methods we prove the bifurcation of periodic traveling water waves -- which are steady in a moving frame -- for {\it all} the values of gravity, surface tension, constant vorticity, depth and wavelenght, extending previous results valid for restricted values of the parameters. We parametrize the bifurcating Stokes waves either with their speed or their momentum.

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  1. Two-dimensional water waves with constant vorticity and general bottom topography

    math.AP 2025-05 conditional novelty 7.0 of 10

    A new operator generalizing the Dirichlet-Neumann operator to constant-vorticity flows over arbitrary bottoms is analyzed, and local well-posedness for the resulting water-wave system is proved.

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