On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions $d\ge 2$

Details On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions $d\ge 2$ On the rigidity of solitary waves for the focusing mass-critical NLS in dimensions $d\ge 2$

2009-02-04

arxiv.org/abs/0902.0802v2

Mathematics

Analysis of PDEs

67 pages

Scientific paper

For the focusing mass-critical NLS $iu_t+\Delta u=-|u|^{\frac 4d}u$, it is conjectured that the only global non-scattering solution with ground state mass must be a solitary wave up to symmetries of the equation. In this paper, we settle the conjecture for $H^1_x$ initial data in dimensions $d=2,3$ with spherical symmetry and $d\ge 4$ with certain splitting-spherically symmetric initial data.

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