The overdamped limit of dynamic density functional theory: Rigorous   results
  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. 
Benjamin D. Goddard, Grigorios A. Pavliotis and Serafim Kalliadasis
math-ph cond-mat.stat-mech math.AP math.MP