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 $i{u}_t+\Delta u=\pm |u{|}^{2}u$ for large spherically symmetric L^2_x(\R^2) 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. We also establish some partial results towards the analogous claims in other dimensions and without the assumption of spherical symmetry.

49 pages, no figures, submitted, Annals of Math. Various corrections

Cited by in corpus (4)

• The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
• Threshold solutions for the focusing 3d cubic Schroedinger equation
• Semilinear Schrödinger Flows on Hyperbolic Spaces: Scattering in H^1
• Characterization of minimal-mass blowup solutions to the focusing mass-critical NLS