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arXiv · 0708.0849

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

Rowan Killip·Monica Visan·Xiaoyi Zhang
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Abstract

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation $iu_t + Δu = \pm |u|^{4/d} u$ for large spherically symmetric L^2_x(R^d) initial data in dimensions $d\geq 3$. 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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Rowan Killip, Monica Visan, Xiaoyi Zhang. 2007-08-06. The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher. https://arxiv.org/abs/0708.0849

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