LINEAR INVISCID DAMPING FOR MONOTONE SHEAR FLOWS

In this article, we prove linear stability, scattering and inviscid damping with optimal decay rates for the linearized 2D Euler equations around a large class of strictly monotone shear flows, (U(y), 0), in a periodic channel under Sobolev perturbations. Here, we consider the settings of both an infinite periodic channel of period L, T-L x R, as well as a finite periodic channel, T-L x [0, 1], 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.