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 2 n−1 <α < 4 n−2 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+ (Rn) ∩H1/2+ (Rn) ∩ H1/2+ ,1(Rn). © 2009 Elsevier Inc. All rights reserved