Dispersive decay for the mass-critical Sch\"odinger equation when $d\geq 3$

Jiabin Qian; Manli Song

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arXiv · 2607.22054

Dispersive decay for the mass-critical Sch\"odinger equation when $d\geq 3$

Jiabin Qian·Manli Song

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Abstract

In this paper we establish the pointwise-in-time dispersive decay for solutions to the mass-critical nonlinear Schr\"odinger 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 $d\geq3$.

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Jiabin Qian, Manli Song. 2026-07-24. Dispersive decay for the mass-critical Sch\"odinger equation when $d\geq 3$. https://arxiv.org/abs/2607.22054

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