# Characterization of Minimal-Mass Blowup Solutions to the Focusing Mass-Critical NLS

@article{Killip2009CharacterizationOM,
title={Characterization of Minimal-Mass Blowup Solutions to the Focusing Mass-Critical NLS},
author={Rowan Killip and Dong Li and Monica Visan and Xiaoyi Zhang},
journal={SIAM J. Math. Anal.},
year={2009},
volume={41},
pages={219-236}
}
• Published 7 April 2008
• Mathematics
• SIAM J. Math. Anal.
Let $d\geq4$ and let u be a global solution to the focusing mass-critical nonlinear Schrodinger equation $iu_t+\Delta u=-|u|^{\frac{4}{d}}u$ with spherically symmetric $H_x^1$ initial data and mass equal to that of the ground state Q. We prove that if u does not scatter, then, up to phase rotation and scaling, u is the solitary wave $e^{it}Q$. Combining this result with that of Merle [Duke Math. J., 69 (1993), pp. 427–453], we obtain that in dimensions $d\geq4$, the only spherically symmetric…

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