On Euler equations and statistical physics
Author(s)
Bibliographic Information
On Euler equations and statistical physics
（Pubblicazioni della Classe di scienze / Scuola Normale Superiore, . Cattedra galileiana）
Scuola Normale Superiore Pubblicazioni della Classe di Scienze, 2008
Ristampa 2008
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Note
Includes bibliographical refereces (p. [67]-69)
Description and Table of Contents
Description
These are a series of lectures given at the 1997 Cattedra Galileiana, at Scuola Normale Superiore. We discuss in these notes two mathematical topics related to Euler equations and turbulence. The general goal is to describe mathematically some coherent structures observed in turbulent flows. The first problem we study concerns 2-dimensional flows: we begin with a system of N points vortices interacting with the natural Coulomb-like force and we consider the associated Gibbs measure. We then show how the measure goes, as N goes to infinity, to a stationary measure which is concentrated on very particular stationary solutions of the two-dimensional Euler equations. We shall study the mathematical properties of these solutions. The second topic we consider is an extension of the previous one to 3-dimensional flows.
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