Existence of gravity-capillary Crapper waves with concentrated vorticity

2021/06/30 by Diego Córdoba, Elena Di Iorio, Córdoba, Diego +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.2106.15923

arxiv created 2021/06/30 · arxiv updated 2021/07/01

Abstract

The aim of this paper is to prove the existence of gravity-capillary Crapper waves with the presence of vorticity. In particular, we consider a concentrated vorticity: point vortex and vortex patch. We show that for small gravity and small vorticity it is possible to demonstrate that the waves are overhanging.

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