The cubic nonlinear Schrödinger equation in two dimensions with radial data

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut + u = ±|u|2 u for large spherically symmetric Lx2(ℝ2) initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state. As a consequence, we deduce that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.