Global existence for some radial, low regularity nonlinear Schrödinger equations (Q2269686)

The nonlinear Schrödinger equation is shown to have a local solution for any energy-subcritical nonlinearity when \(u_0\) is the characteristic function of a ball in \(\mathbb R^n\). The existence of a global solution for \(n\geq3\) and for certain restrictions on the nonlinearity is also established. Finally, the existence of a global solution is established when the initial function is radial of a certain class and the nonlinear Schrödinger equation has an energy-subcritical nonlinearity.