Linear inviscid damping near monotone shear flows

TL;DR

This paper provides an elementary proof of sharp decay rates and precise asymptotics for linear inviscid damping near monotone shear flows in a periodic channel, refining previous results.

Contribution

It offers a simplified proof and detailed asymptotic analysis of linear inviscid damping near monotone shear flows, improving understanding of decay behavior.

Findings

Established sharp decay rates for solutions

Derived precise asymptotics in L-infinity space

Confirmed previous results with a more elementary approach

Abstract

We give an elementary proof of sharp decay rates and the linear inviscid damping near monotone shear flow in a periodic channel, first obtained in [14]. We shall also obtain the precise asymptotics of the solutions, measured in the space $L^{\infty}$.