Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iu_t + Δu = ±|u|^{4 ∕ d}u for large spherically symmetric L_x²(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.

Keywords

Nonlinear Schrödinger equation, mass-critical, focusing

Mathematical Subject Classification

Primary: 35Q55

Authors