Rough log-log blowup solutions to mass-critical NLS in higher dimensions $d\ge 3$

Abstract

We study the stability of the log--log blow-up regime for the focusing mass-critical nonlinear Schrödinger equation under small $H^s$ perturbations. Previously, stability was established for every $0<s<1$ in dimension two by Colliander and Raphaël [Math. Ann. (2009)] and subsequently extended to dimensions $d\ge 3$ under the restriction $s>1/(1+\min \{1,4/d\})$ by Sun and the fourth author [J. Math. Pures Appl. (2020)]. We remove this restriction and establish stability throughout the full subcritical range $0<s<1$.