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arXiv · 1211.3314

Traveling water waves with compactly supported vorticity

Jalal Shatah·Samuel Walsh·Chongchun Zeng
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Abstract

In this paper, we prove the existence of two-dimensional, traveling, 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.

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Jalal Shatah, Samuel Walsh, Chongchun Zeng. 2012-11-14. Traveling water waves with compactly supported vorticity. https://doi.org/10.1088/0951-7715%2F26%2F6%2F1529

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