Linear Inviscid Damping for a Class of Monotone Shear Flow in Sobolev Spaces

Abstract In this paper, we prove the decay estimates of the velocity and H 1 scattering for the two‐dimensional linearized Euler equations around a class of monotone shear flow in a finite channel. Our result is consistent with the decay rate predicted by Case in 1960. © 2016 Wiley Periodicals, Inc.