In this talk we will discuss joint work with Thomas Chen on the dynamics of a boson gas with three-body interactions in dimensions d = 1,2. We prove that in the limit as the particle number N tends to infinity, the BBGKY hierarchy of k-particle marginals converges to a limiting Gross-Pitaevskii (GP) hierarchy for which we prove existence and uniqueness of solutions. For factorized initial data, the solutions of the GP hierarchy are shown to be determined by solutions of a quintic nonlinear Schrödinger equation.

Time permitting, we will briefly describe our new approach for studying well-posedness of the Cauchy problem for focusing and defocusing GP hierarchy.