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

Jiabin Qian; Manli Song

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

Analysis of PDEs 2026-07-24 v1

Authors: Jiabin Qian , Manli Song

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 $d\geq3$ .

Keywords

dispersive decay mass-critical Schrödinger equation nonlinear Schrödinger equation pointwise estimate high dimension

Cite

@article{arxiv.2607.22054,
  title  = {Dispersive decay for the mass-critical Sch\"odinger equation when $d\geq 3$},
  author = {Jiabin Qian and Manli Song},
  journal= {arXiv preprint arXiv:2607.22054},
  year   = {2026}
}