Mathematics – Analysis of PDEs

Scientific paper

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2008-04-07

Mathematics

Analysis of PDEs

17 pages

Scientific paper

Let $d\geq 4$ and let $u$ be a global solution to the focusing mass-critical nonlinear Schr\"odinger equation $iu_t+\Delta u=-|u|^{\frac 4d}u$ 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 \cite{merle2}, we obtain that in dimensions $d\geq 4$, the only spherically symmetric minimal-mass blowup solutions are, up to phase rotation and scaling, the pseudo-conformal ground state and the solitary wave.

**Killip Rowan**

Physics – Mathematical Physics

Scientist

**Li Dong**

Mathematics – Dynamical Systems

Scientist

**Visan Monica**

Mathematics – Analysis of PDEs

Scientist

**Zhang Xiaoyi**

Mathematics – Analysis of PDEs

Scientist

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