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We consider the stationary Stokes problem in a three-dimensional fluid domain$\mathcal F$ with non-homogeneous Dirichlet boundary conditions. We assume thatthis fluid domain is the complement of a bounded obstacle $\mathcal B$ in abounded or an exterior smooth container $\Omega$. We compute sharp asymptoticsof the solution to the Stokes problem when the distance between the obstacleand the container boundary is small.

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