Stationary inviscid limit to shear flows

In this article we establish a density result for certain stationary shear flows, mu(y), that vanish at the vertical boundaries of a box. We construct stationary solutions to 2D Navier-Stokes that are epsilon-close in L-infinity to the given shear flow. Our construction is based on a coercivity estimate for the Rayleigh operator, R[v], which is based on a decomposition made possible by the vanishing of mu at the boundaries. As a corollary, we obtain, for each epsilon < < 1, a one parameter family of solutions to the NS(epsilon) system which approximate the Couette flow. (C) 2019 Elsevier Inc. All rights reserved.