Abstract
In this paper, we establish the existence of time quasi-periodic
solutions to generalized surface quasi-geostrophic equation $({\rm
gSQG})_\alpha$ in the patch form close to Rankine vortices. We show that
invariant tori survive when the order $\alpha$ of the singular operator
belongs to a Cantor set contained in $(0,\frac12)$ with almost full
Lebesgue measure. The proof is based on several techniques from KAM
theory, pseudo-differential calculus together with Nash-Moser scheme in
the spirit of the recent works \cite{Baldi-Berti2018,Berti-Bolle15}. One
key novelty here is a refined Egorov type theorem established through a
new approach based on the kernel dynamics together with some hidden
Töpliz structures.
Original language | English (US) |
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Journal | havard.edu |
State | Published - Oct 1 2021 |
Keywords
- Mathematics - Analysis of PDEs