GIBBS EQUILIBRIUM FLUCTUATIONS OF POINT VORTEX DYNAMICS

• 成果类型: Article
• 署名作者: Grotto, Francesco; Luongo, Eliseo; Romito, Marco
• 署名单位: University of Pisa; Scuola Normale Superiore di Pisa
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2095
• 发表日期: 2024
• 页码: 5426-5461
• 关键词: 2-dimensional euler equations; weak vorticity-formulation; singular initial data; statistical-mechanics; 2d euler; stationary flows; EVOLUTION; propagation; EXISTENCE; chaos

摘要

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 >= 0. We prove that the space-time fluctuation field around the (constant) mean field limit satisfies when N -> infinity a generalized version of two-dimensional Euler dynamics preserving the Gaussian energyenstrophy ensemble.