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arXiv · 2308.00163

Gibbs Equilibrium Fluctuations of Point Vortex Dynamics

Francesco Grotto·Eliseo Luongo·Marco Romito
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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 $\beta\geq 0$. We prove that the space-time fluctuation field around the (constant) Mean Field limit satisfies when $N\to\infty$ a generalized version of 2-dimensional Euler dynamics preserving the Gaussian Energy-Enstrophy ensemble.

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Francesco Grotto, Eliseo Luongo, Marco Romito. 2023-07-31. Gibbs Equilibrium Fluctuations of Point Vortex Dynamics. https://doi.org/10.1214/24-aap2095

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