Global well-posedness and scattering for nonlinear Schr{ö}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.

38 pages