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Stefano Pasquali: Asymmetrical three-dimensional Water Waves on Beltrami flows

Time: Thu 2023-09-21 14.00 - 15.00

Location: Institut Mittag-Leffler, Seminar Hall Kuskvillan and Zoom

Video link: Meeting ID: 921 756 1880

Participating: Stefano Pasquali, Université Paris-Saclay

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In this talk we prove the existence of small amplitude three-dimensional doubly periodic steady water waves with vorticity. The domain of the fluid has finite depth, and pattern of the waves is non-symmetric with respect to the propagation direction of the waves; moreover, the relative velocity field is a Beltrami field, meaning that the vorticity is proportional to the velocity. The main difficulty arises from the presence of vorticity, which in turn leads to a careful study of a generalized Dirichlet–Neumann operator; moreover, in the case of vanishing surface tension, we have to overcome small-divisors issues.

This is a joint work with M. Groves (Saarland University), D. Nilsson and E. Wahlén (Lund University).