A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
type: Item
instance of: scholarly article
title: A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
zbMATH Open document ID: 0745.76001
DOI: 10.1007/BF02099262
published in: Communications in Mathematical Physics
publication date: 1992-09-26T00:00:00Z
review text: We consider the canonical Gibbs measure associated to an \(N\)-vortex system in a bounded domain \(\Lambda\), at inverse temperature \(\tilde\beta\) and prove that, in the limit \(N\to\infty\), \(\tilde\beta/N\to\beta\), \(\alpha N\to1\), where \(\beta\in(-8\pi,+\infty)\) (here \(\alpha\) denotes the vorticity intensity of each vortex), the one particle distribution function \(\rho^ N=\rho^ N(x)\), \(x\in\Lambda\) converges to a superposition of solutions \(\rho_ \beta\) of the mean field equation. Finally, we discuss a possible connection of the present analysis with the \(2-D\) turbulence.
Mathematics Subject Classification ID: 76A02
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 82D15
zbMATH DE Number: 54724
zbMATH Keywords: canonical Gibbs measure
zbMATH Keywords: \(N\)-vortex system
zbMATH Keywords: one particle distribution function
zbMATH Keywords: mean field equation
zbMATH Keywords: \(2-D\) turbulence
author: Emanuele Caglioti
author: P.-L. Lions
author: Carlo Marchioro
author: Mario Pulvirenti
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 54724