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Seminar on Analysis, Geometry, and PDEs


Tid: 2021-10-19 15:15 till 16:15
Plats: The talk is given on Zoom. If you wish to receive a link, please contact the organizer.
Kontakt: eskil [dot] rydhe [at] math [dot] lu [dot] se
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Traveling quasi-periodic water waves with constant vorticity

Speaker: Luca Franzoi, New York University Abu Dhabi

Abstract: In this talk I will present two bifurcation results of time quasi-periodic traveling wave solutions for space periodic water waves with constant vorticity. In particular, I will show the existence of small amplitude time quasi-periodic solutions for a bidimensional fluid over a flat bottom delimited by a space-periodic free interface. Both the cases when the surface tension at the free boundary is neglected or not are considered. These quasi-periodic solutions are constructed using a Nash-Moser implicit function iterative scheme and exist for most values of some parameters in Borel sets of asymptotically full Lebesgue measure. I will also focus on the differences between the gravity-capillary and the pure gravity cases. These are joint works with Massimiliano Berti and Alberto Maspero.