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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/226294For the focusing mass-critical NLS $iu_t+Δu=-|u|^{\frac 4d}u$, 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.67 pagesAnalysis of PDEsOn the rigidity of solitary waves for the focusing mass-critical NLS in dimensions $d\ge 2$text