Recurrence in 2D Inviscid Channel Flow

TL;DR

This paper proves a recurrence theorem for 2D inviscid channel flow solutions, showing they repeatedly return close to initial states in a specific mathematical sense, extending previous results on 2D Euler equations.

Contribution

It extends earlier recurrence results to 2D inviscid channel flow with periodic boundary conditions along one direction.

Findings

Solutions return arbitrarily close to initial states repeatedly

Extension of previous recurrence results to channel flow

Applicable for solutions in Sobolev space H^s with s>2

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 $H^0$ 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.