Quadratic Morawetz inequalities and asymptotic completeness in the   energy space for nonlinear Schr"odinger and Hartree equations
  Recently several authors have developed multilinear and in particular quadratic extensions of the classical Morawetz inequality. Those extensions provide (among other results) an easy proof of asymptotic completeness in the energy space for nonlinear Schr"odinger equations in arbitrary space dimension and for Hartree equations in space dimension greater than two in the noncritical cases. We give a pedagogical review of the latter results. 
J. Ginibre, G. Velo