We consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the canonical Gibbs ensemble at inverse temperature β≥0. We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when N→∞ a generalized version of two-dimensional Euler dynamics preserving the Gaussian energy-enstrophy ensemble.
Gibbs equilibrium fluctuations of point vortex dynamics
Grotto, Francesco;Romito, Marco
2024-01-01
Abstract
We consider a system of N point vortices in a bounded domain with null total circulation, whose statistics are given by the canonical Gibbs ensemble at inverse temperature β≥0. We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when N→∞ a generalized version of two-dimensional Euler dynamics preserving the Gaussian energy-enstrophy ensemble.File in questo prodotto:
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