Navier wall law for nonstationary viscous incompressible flows

We study the Navier wall law for the two-dimensional initial boundary value problem of the Navier–Stokes equations in a domain with a rough boundary. The Navier wall law is verified for the initial data in C1C1 class under the natural compatibility condition. Our proof relies on the boundary layer analysis and the L∞L∞ theory of the Navier–Stokes equations in the half space.