  We study the existence and the uniqueness of a solution $\fy$ to the linear
Fokker-Planck equation $-\Delta \fy + \div(\fy \F) = f$ in a bounded domain of
$\R^d$ when $\F$ is a "confinement" vector field acting for instance like the
inverse of the distance to the boundary. An illustration of the obtained
results is given within the framework of fluid mechanics and polymer flows.
