On circular flows: linear stability and damping

TL;DR

This paper proves optimal decay rates for linear inviscid damping around 2D Taylor-Couette flow in an annular domain, extending stability results to weighted norms and describing boundary singularity formation.

Contribution

It establishes linear inviscid damping with optimal decay rates for 2D Taylor-Couette flow in an annular domain, including stability in weighted norms and boundary blow-up behavior.

Findings

Optimal decay rates for linear inviscid damping

Stability in weighted norms allowing boundary singularities

Description of boundary blow-up behavior

Abstract

In this article we establish linear inviscid damping with optimal decay rates around 2D Taylor-Couette flow and similar monotone flows in an annular domain $B_{r_{2}}(0) \setminus B_{r_{1}}(0) \subset \mathbb{R}^{2}$. Following recent results by Wei, Zhang and Zhao, we establish stability in weighted norms, which allow for a singularity formation at the boundary, and additional provide a description of the blow-up behavior.