Global well-posedness and scattering for nonlinear Schr{\"o}dinger equations with algebraic nonlinearity when $d = 2, 3$, $u_{0}$ radial

Abstract

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.