The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrodinger equation iut+Δu=±|u|4∕du for large spherically symmetric Lx2(ℝd) 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.