  We investigate regularity estimates for the stationary Navier-Stokes
equations above a highly oscillating Lipschitz boundary with the no-slip
boundary condition. Our main result is an improved Lipschitz regularity
estimate at scales larger than the boundary layer thickness. We also obtain an
improved $C^{1,\mu}$ estimate and identify the building blocks of the
regularity theory, dubbed `Navier polynomials'. In the case when some structure
is assumed on the oscillations of the boundary, for instance periodicity, these
estimates can be seen as local error estimates. Although we handle the
regularity of the nonlinear stationary Navier-Stokes equations, our results do
not require any smallness assumption on the solutions.
