  We study the evolution of a many-particle system whose wave function obeys
the N-body Schroedinger equation under Bose symmetry. The system Hamiltonian
describes pairwise particle interactions in the absence of an external
potential. We derive apriori dispersive estimates that express the overall
repulsive nature of the particle interactions. These estimates hold for a wide
class of two-body interaction potentials which are independent of the particle
number, N. We discuss applications of these estimates to the BBGKY hierarchy
for reduced density matrices analyzed by Elgart, Erdos, Schlein and Yau.
