  Consider the overdamped limit for a system of interacting particles in the
presence of hydrodynamic interactions. For two-body hydrodynamic interactions
and one- and two-body potentials, a Smoluchowski-type evolution equation is
rigorously derived for the one-particle distribution function. This new
equation includes a novel definition of the diffusion tensor. A comparison with
existing formulations of dynamic density functional theory is also made.
