Traveling waves near Poiseuille flow for the 2D Euler equation

TL;DR

This paper discovers a broad family of nontrivial traveling wave solutions for the 2D Euler equation close to Poiseuille flow, expanding understanding of fluid dynamics near laminar flows.

Contribution

It introduces a large family of Lipschitz traveling waves for the 2D Euler equation near Poiseuille flow in low regularity spaces, which was previously unknown.

Findings

Existence of new traveling wave solutions near Poiseuille flow.

Solutions are Lipschitz continuous in vorticity space.

Results apply at arbitrarily small distances in $H^s$ with $s<3/2$.

Abstract

In this paper we reveal the existence of a large family of new, nontrivial and Lipschitz traveling waves for the 2D Euler equation at an arbitrarily small distance from the Poiseuille flow in $H^s$, with $s<3/2$, at the level of the vorticity.