当d≥3时质量临界薛定谔方程的色散衰减
Dispersive decay for the mass-critical Schödinger equation when $d\geq 3$
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中文总结 AI 辅助
研究d≥3时质量临界薛定谔方程解的逐时色散衰减，通过非线性项精细分解和改进线性估计控制非线性贡献，统一框架将相关基础结果扩展到高维设置。
中文摘要 AI 辅助
本文建立了空间维数d≥3时质量临界非线性薛定谔方程解的逐时色散衰减。我们的论证依赖于非线性项的精细分解和改进的线性估计，这使我们能够控制非线性贡献。这项工作统一了一个框架，将Fan、Killip、Visan和Zhao早期论文中针对d = 1、2、3的相同问题的基础结果扩展到一般高维设置d≥3。
英文摘要
In this paper we establish the pointwise-in-time dispersive decay for solutions to the mass-critical nonlinear Schrödinger equation in spatial dimensions $d\geq3$. Our argument relies on a delicate decomposition of the nonlinearity and an improved linear estimate, which together enable us to control the nonlinear contribution. This work unifies a framework for extending the foundational results established in an earlier paper by Fan, Killip, Visan, and Zhao [Math. Z. \textbf{311}(1), Paper No. 21, 16 pp (2025)], where the same problem was addressed for spatial dimensions $d=1,2,3$, to the general higher-dimensional setting $d\geq3$.
