Why viscous fluids adhere to rugose walls:: A mathematical explanation

The main purpose of this paper is to justify rigorously the following assertion: A viscous fluid cannot slip on a wall covered by microscopic asperities because, due to the viscous dissipation, the surface irregularities bring to rest the fluid particles in contact with the wall. In mathematical terms, this corresponds to an asymptotic property established in this paper for any family of fields that slip on oscillating boundaries and remain uniformly bounded in the H1-norm.