On the asymptotic limit of the Navier–Stokes system on domains with rough boundaries

We study the asymptotic behavior of solutions to the incompressible Navier–Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are non-degenerate, meaning not oriented in a single direction.