Title: The Vanishing viscosity limit for some symmetric flows,
Abstract: The focus of this paper is on the analysis of the boundary layer and the
associated vanishing viscosity limit for two classes of flows with symmetry,
namely, Plane-Parallel Channel Flows and Parallel Pipe Flows. We construct
explicit boundary layer correctors, which approximate the difference between
the Navier-Stokes and the Euler solutions. Using properties of these
correctors, we establish convergence of the Navier-Stokes solution to the Euler
solution as viscosity vanishes with optimal rates of convergence. In addition,
we investigate vorticity production on the boundary in the limit of vanishing
viscosity. Our work significantly extends prior work in the literature.