发表机构
Institute of Applied Physics and Computational Mathematics; School of Mathematics and Physics, University of Science and Technology Beijing（应用物理与计算力学研究所; 北京科技大学数学与物理学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究聚焦质量临界非线性薛定谔方程在小扰动下对数-对数爆破解的稳定性，移除先前维数限制，将稳定性推广到所有次临界指数范围。
AI 中文摘要
我们研究聚焦质量临界非线性薛定谔方程在小 $H^s$ 扰动下对数-对数爆破机制的稳定性。此前，Colliander 和 Raphaël [Math. Ann. (2009)] 在二维中建立了对所有 $0<s<1$ 的稳定性，随后 Sun 和第四作者 [J. Math. Pures Appl. (2020)] 在限制 $s>1/(1+\min\{1,4/d\})$ 下将其推广到维数 $d\geq3$。我们移除了这一限制，并在整个次临界范围 $0<s<1$ 内建立了稳定性。
英文摘要
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 $d\geq3$ 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 $0<s<1$.
