Zineb Hassainia

New York University Abu Dhabi

Time quasi-periodic vortex patches

In this talk I will discuss the existence of quasi-periodic solutions for the 2D-Euler equations. Using a Nash-Moser implicit function iterative scheme, we show the emergence of quasi-periodic vortex patch structures close to Kirchhoff elliptical vortices when the aspect ratios belongs to a Cantor set with almost full Lebesgue measure. The study of the linearized operators at each step of the iteration is based on pseudo-differential operator techniques and a KAM reducibility scheme. This is a joint work with Massimiliano Berti and Nader Masmoudi.