Justification of lubrication approximation: An application to fluid/solid interactions

We consider the stationary Stokes problem in a three-dimensional fluid domain F with non-homogeneous Dirichlet boundary conditions. We assume that this fluid domain is the complement of a bounded obstacle B in a bounded or an exterior smooth container Omega. We compute sharp asymptotics of the solution to the Stokes problem when the distance between the obstacle and the container boundary is small.