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

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.

Categories: math.AP