Recently there has been much interest in damping phenomena for kinetic equations following the seminal works of Mouhot-Villani on Landau damping and of Bedrossian-Masmoudi on inviscid damping around Couette flow.

In this talk I present some of the main results of my PhD thesis on linear inviscid damping for the 2D Euler equations around general monotone shear  flows in the framework of Sobolev regularity.

Here I consider both the settings of an infinite periodic channel and a finite periodic channel with impermeable walls.

The latter setting is shown to not only be technically more challenging, but to exhibit qualitatively different behavior due to boundary effects.