Global well-posedness and scattering for nonlinear Schrödinger equations with algebraic nonlinearity when $d = 2,3$ and $u_0$ is radial

Abstract

In this paper we discuss global well-posedness and scattering for some initial value problems that are ˙ H 1 subcritical. We prove global well-posedness and scattering for radial data in H s , s > s c , where the initial value problem is ˙ H s c -critical. We make use of the long time Strichartz estimates of [13] to do this.