The Poincaré Recurrence Problem of Inviscid Incompressible Fluids

2007/07/30 by Y. Charles Li, Li, Y. Charles · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Quantum chaos and dynamical systems #math-ph #math.AP #math.DS #math.MP #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.0707.4456

arxiv created 2007/07/30 · openalex publication_date 2007/07/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Nadirashvili presented a beautiful example showing that the Poincaré recurrence does not occur near a particular solution to the 2D Euler equation of inviscid incompressible fluids. Unfortunately, Nadirashvili's setup of the phase space is not appropriate, and details of the proof are missing. This note fixes that.

Cited by

• Issues of Chaos and Recurrence in Infinite Dimensions

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