Time periodic solutions for the 2D Euler equation near Taylor-Couette flow

TL;DR

This paper proves the existence of smooth, time-periodic solutions to the 2D Euler equations near Taylor-Couette flow in an annular domain, expanding understanding of fluid dynamics stability.

Contribution

It demonstrates the existence of non-trivial, smooth, time-periodic solutions close to Taylor-Couette flow in a specific Sobolev space, advancing theoretical fluid dynamics.

Findings

Existence of time-periodic solutions near Taylor-Couette flow

Solutions are smooth and non-trivial

Results hold at low regularity in $H^s$, with $s<3/2"

Abstract

In this paper we consider the incompressible 2D Euler equation in an annular domain with non-penetration boundary condition. In this setting, we prove the existence of a family of non-trivially smooth time-periodic solutions at an arbitrarily small distance from the stationary Taylor-Couette flow in $H^s$, with $s<3/2$, at the vorticity level.