In this paper, we investigate the dynamics of a system of
N weakly interacting bosons with singular three-body interactions in three dimensions. By assuming factorized initial data
ΨN,0=φ0⊗N and triple collisions, we prove that in the many-particle limit, its mean-field approximation converges to quintic Hartree dynamics. Moreover, we prove that the rate of convergence towards the mean-field quintic Hartree evolution is of
O(N−(1+4a)/(3+2a)) for
φ0∈H(3/2)+a(R3) where
0≤a<1/2 and
O(N−1) for
a>1. Our proof is based on and extends the Fock space approach.