Nonlinear inviscid damping for a class of monotone shear flows in finite channel

TL;DR

This paper proves nonlinear inviscid damping for certain monotone shear flows in a finite channel, using wave operators and Gevrey class initial conditions, advancing understanding of flow stability.

Contribution

It introduces a novel approach using wave operators of a modified Rayleigh operator to establish nonlinear damping in finite channels for Gevrey-class perturbations.

Findings

Nonlinear inviscid damping is proven for specific shear flows.

The method applies to initial perturbations in Gevrey-$1/s$ class with $s>2$.

The approach utilizes a wave operator framework in a tailored coordinate system.

Abstract

We prove the nonlinear inviscid damping for a class of monotone shear flows in $T\times [0,1]$ for initial perturbation in Gevrey-$1/s$($s>2$) class with compact support. The main idea of the proof is to use the wave operator of a slightly modified Rayleigh operator in a well chosen coordinate system.