Global existence for some radial, low regularity nonlinear Schrödinger equations

We prove the nonlinear Schrödinger equation has a local solution for any energy – subcritical nonlinearity when u0 is the characteristic function of a ball in Rn. Additionally, we establish the existence of a global solution for n⩾3 when and α⩽2. Finally, we establish the existence of a global solution when the initial function is radial, the nonlinear Schrödinger equation has an energy subcritical nonlinearity, and the initial function lies in Hρ+ϵ(Rn)∩H1/2+ϵ(Rn)∩H1/2+ϵ,1(Rn).