  We consider the stationary Stokes problem in a three-dimensional fluid domain
$\mathcal F$ with non-homogeneous Dirichlet boundary conditions. We assume that
this fluid domain is the complement of a bounded obstacle $\mathcal B$ 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.
