Dispersive decay for the mass-critical Schödinger equation when d≥ 3

2026/07/24 by Jiabin Qian, Manli Song
#math.AP

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Abstract

In this paper we establish the pointwise-in-time dispersive decay for solutions to the mass-critical nonlinear Schrödinger equation in spatial dimensions d≥3. 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. 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≥3.

Citations

• Uniform decay estimates and the lorentz invariance of the classical wave equation

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