article published yes Rowan Killip author Terence Tao author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iu t ​ +Δu=±∣u∣ 2 u for large spherically symmetric L x 2 ​ (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. European Mathematical Society Press2009 eng 1435-9855 1435-9863 0707.318810.4171/jems/180 1161203-1258 yes Killip, Rowan, Terence Tao, and Monica Vişan. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press, 2009. <a href="https://doi.org/10.4171/jems/180">https://doi.org/10.4171/jems/180</a>. R. Killip, T. Tao, and M. Vişan, “The cubic nonlinear Schrödinger equation in two dimensions with radial data,” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6. European Mathematical Society Press, pp. 1203–1258, 2009. Killip, R., Tao, T., &#38; Vişan, M. (2009). The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. European Mathematical Society Press. <a href="https://doi.org/10.4171/jems/180">https://doi.org/10.4171/jems/180</a> Killip R, Tao T, Vişan M. The cubic nonlinear Schrödinger equation in two dimensions with radial data. <i>Journal of the European Mathematical Society</i>. 2009;11(6):1203-1258. doi:<a href="https://doi.org/10.4171/jems/180">10.4171/jems/180</a> Killip, Rowan, et al. “The Cubic Nonlinear Schrödinger Equation in Two Dimensions with Radial Data.” <i>Journal of the European Mathematical Society</i>, vol. 11, no. 6, European Mathematical Society Press, 2009, pp. 1203–58, doi:<a href="https://doi.org/10.4171/jems/180">10.4171/jems/180</a>. R. Killip, T. Tao, M. Vişan, Journal of the European Mathematical Society 11 (2009) 1203–1258. Killip R, Tao T, Vişan M. 2009. The cubic nonlinear Schrödinger equation in two dimensions with radial data. Journal of the European Mathematical Society. 11(6), 1203–1258. 220902026-06-19T08:49:58Z2026-07-01T12:57:57Z