Stationary Inviscid Limit to Shear Flows

In this note we establish a density result for certain stationary shear flows, $\mu (y)$, that vanish at the boundaries of a horizontal channel. We construct stationary solutions to 2D Navier-Stokes that are $ϵ$-close in $L^{\mathrm{\infty }}$ 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.