Recurrence in 2D Inviscid Channel Flow

2010/09/08 by Y. Charles Li, Li, Y. Charles
Computer Science · Mathematics · Physics and Astronomy · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Mathematical Dynamics and Fractals #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.DS #math.MP #nlin.CD #physics.flu-dyn

paper · pdf · doi:10.48550/arxiv.1009.1576

arxiv created 2010/09/08 · openalex publication_date 2010/09/08 · arxiv updated 2010/09/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

I will prove a recurrence theorem which says that any H^s (s>2) solution to the 2D inviscid channel flow returns repeatedly to an arbitrarily small H⁰ neighborhood. Periodic boundary condition is imposed along the stream-wise direction. The result is an extension of an early result of the author [Li, 09] on 2D Euler equation under periodic boundary conditions along both directions.

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