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

Abstract

For the focusing mass-critical NLS $i{u}_t+\Delta u=-|u{|}^{\frac{4}{d}}u$, 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 $H_x^1$ initial data in dimensions $d=2,3$ with spherical symmetry and $d\ge 4$ with certain splitting-spherically symmetric initial data.

67 pages

References in corpus (3)

• The mass-critical nonlinear Schrödinger equation with radial data in dimensions three and higher
• The cubic nonlinear Schrödinger equation in two dimensions with radial data
• Minimal-mass blowup solutions of the mass-critical NLS

Cited by in corpus (1)

• The instability of Bourgain-Wang solutions for the L^2 critical NLS