Invariant KAM tori around annular vortex patches for 2D Euler equations
Analysis of PDEs
2023-02-03 v1 Dynamical Systems
Fluid Dynamics
Abstract
We construct time quasi-periodic vortex patch solutions with one hole for the planar Euler equations. These structures are captured close to any annulus provided that its modulus belongs to a massive Borel set. The proof is based on Nash-Moser scheme and KAM theory applied with a Hamiltonian system governing the radial deformations of the patch. Compared to the scalar case, some technical issues emerge due to the interaction between the interfaces. One of them is related to a new small divisor problem in the second order Melnikov non-resonances condition coming from the transport equations advected with different velocities.
Keywords
Cite
@article{arxiv.2302.01311,
title = {Invariant KAM tori around annular vortex patches for 2D Euler equations},
author = {Zineb Hassainia and Taoufik Hmidi and Emeric Roulley},
journal= {arXiv preprint arXiv:2302.01311},
year = {2023}
}
Comments
107 pages