Vol. 1, No. 2, 2008

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The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher

Rowan Killip, Monica Visan and Xiaoyi Zhang

Vol. 1 (2008), No. 2, 229–266
Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation $i{u}_{t}+\Delta u=±|u{|}^{4∕d}u$ for large spherically symmetric ${L}_{x}^{2}\left({ℝ}^{d}\right)$ 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.

Keywords
Nonlinear Schrödinger equation, mass-critical, focusing
Primary: 35Q55