PreprintarXiv licencearXiv
Rough log-log blowup solutions to mass-critical NLS in higher dimensions d≥ 3
Abstract
We study the stability of the log--log blow-up regime for the focusing mass-critical nonlinear Schrödinger equation under small Hs 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≥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.
Related
- Classification of minimal-mass blowup solutions to the mass-critical Hartree equation at the L2-critical level
- Blowup of smooth solutions to 2D quasilinear wave equations with higher-order null conditions and short pulse initial data
- Isolated singularities of solutions to the Yamabe equation in higher dimensions I
- Infinite time blow-up of solutions to the classical Keller-Segel model of chemotaxis in higher dimensions
- Vanishing orders of Dirichlet solutions to the Schrödinger equation in dimensions three and higher
BibTeX
@misc{ma2026rough,
title = {{Rough log-log blowup solutions to mass-critical NLS in higher dimensions $d\geq 3$}},
author = {Zuyu Ma and Changxing Miao and Yilin Song and Jiqiang Zheng},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29818},
eprint = {2609.29818},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29818},
}
RIS
TY - UNPB
TI - Rough log-log blowup solutions to mass-critical NLS in higher dimensions d≥ 3
AU - Zuyu Ma
AU - Changxing Miao
AU - Yilin Song
AU - Jiqiang Zheng
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29818
UR - https://arxiv.org/abs/2609.29818
AB - 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≥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.
ER -