The Mass-critical Nonlinear Schrödinger Equation with Radial Data in Dimensions Three and Higher

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut+∆u = ±|u|4/du for large spherically symmetric Lx(R d) initial data in dimensions d ≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solution must concentrate at least the mass of the ground state at the blowup time.