  We study the defocusing nonlinear Schr\"odinger equation in three space
dimensions. We prove that any radial solution that remains bounded in the
critical Sobolev space must be global and scatter. In the energy-supercritical
setting, we employ a space-localized Lin--Strauss Morawetz inequality of
Bourgain. In the inter-critical regime, we prove long-time Strichartz estimates
and frequency-localized Lin--Strauss Morawetz inequalities.
