Periodic and quasi-periodic Euler-α flows close to Rankine vortices

2022/08/28 by Roulley, Emeric
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2208.13109

Abstract

In the present contribution, we first prove the existence of m-fold simply-connected V-states close to the unit disc for Euler-α equations. These solutions are implicitly obtained as bifurcation curves from the circular patches. We also prove the existence of quasi-periodic in time vortex patches close to the Rankine vortices provided that the scale parameter α belongs to a suitable Cantor-like set of almost full Lebesgue measure. The techniques used to prove this result are borrowed from the Berti-Bolle theory in the context of KAM for PDEs.

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