Title: Green function for linearized Navier-Stokes around a boundary layer profile: away from critical layers,
Abstract: In this paper, we construct the Green function for the classical
Orr-Sommerfeld equations, which are the linearized Navier-Stokes equations
around a boundary layer profile. As an immediate application, we derive uniform
sharp bounds on the semigroup of the linearized Navier-Stokes problem around
unstable profiles in the vanishing viscosity limit.