  In this paper we study the hydrodynamic (small mass approximation) limit of a
Fokker-Planck equation. This equation arises in the kinetic description of the
evolution of a particle system immersed in a viscous Stokes flow. We discuss
two different methods of hydrodynamic convergence. The first method works with
initial data in a weighted L2 space and uses weak convergence and the
extraction of convergent subsequences. The second uses entropic initial data
and gives an L1 convergence to the solution of the limit problem via the study
of the relative entropy.
