  In this paper we discuss global well - posedness and scattering for some
initial value problems that are $L^{2}$ supercritical and $\dot{H}^{1}$
subcritical, with radial data. We prove global well - posedness and scattering
for radial data in $H^{s}$, $s > s_{c}$, where the problem is $\dot{H}^{s_{c}}$
- critical. We make use of the long time Strichartz estimates of \cite{D2} to
do this.

Analysis of PDEs