  We consider a system of interacting particles subjected to Langevin inertial
dynamics and derive the governing time-dependent equation for the one-body
density. We show that, after suitable truncations of the
Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy, and a multiple time scale
analysis, we obtain a self-consistent equation involving only the one-body
density. This study extends to arbitrary dimensions previous work on a
one-dimensional fluid and highlights the subtelties of kinetic theory in the
derivation of dynamical density functional theory.
