# Linear inviscid damping in Gevrey spaces

## TL;DR

This paper proves linear inviscid damping for a broad class of shear flows in Gevrey spaces, advancing the understanding of stability in 2D Euler equations and paving the way for nonlinear results.

## Contribution

It establishes linear inviscid damping near general monotone shear flows in Gevrey spaces, a key step towards nonlinear damping for non-Couette flows.

## Key findings

- Proves linear inviscid damping in Gevrey spaces for general shear flows.
- Extends stability analysis beyond the classical Couette flow.
- Provides foundational results for nonlinear inviscid damping in 2D Euler equations.

## Abstract

We prove linear inviscid damping near a general class of monotone shear flows in a finite channel, in Gevrey spaces. It is an essential step towards proving nonlinear inviscid damping for general shear flows that are not close to the Couette flow, which is a major open problem in 2d Euler equations.