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 Schrödinger equation $i{u}_t+\Delta u=\pm |u{|}^{4/d}u$ for large spherically symmetric L^2_x(R^d) initial data in dimensions $d\ge 3$. 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.

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• Threshold solutions for the focusing 3d cubic Schroedinger equation
• The nonlinear Schrödinger equations with combined nonlinearities of power-type and Hartree
• Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS