Multilinear Morawetz identities for the Gross-Pitaevskii hierarchy

This article consists of two parts. In the first part, we review the most recent proofs establishing quadratic Morawetz inequalities for the nonlinear Schr"odinger equation (NLS). We also describe the applications of these estimates to the problem of quantum scattering. In the second part, we generalize some of the methods developed for the NLS by many authors to the case of Gross-Pitaevskii (GP) hierarchies. In particular, we prove both regular and interaction Morawetz identities for the GP hierarchy, which appear here for the first time in the literature.