# The cubic nonlinear Schrödinger equation in two dimensions with radial data

### Rowan Killip

University of California Los Angeles, United States### Terence Tao

University of California Los Angeles, United States### Monica Vișan

University of California Los Angeles, United States

## Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation *iut* + *u* = ±|*u*|2 *u* for large spherically symmetric _L__x_2(ℝ2) 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.

## Cite this article

Rowan Killip, Terence Tao, Monica Vișan, The cubic nonlinear Schrödinger equation in two dimensions with radial data. J. Eur. Math. Soc. 11 (2009), no. 6, pp. 1203–1258

DOI 10.4171/JEMS/180