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

International audienceWe 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