Dispersive decay for the Inter-critical nonlinear Schr\"{o}dinger equation in $\mathbb{R}^3$

Boyu Jiang; Jiawei Shen; Kexue Li

Dispersive decay for the Inter-critical nonlinear Schr\"{o}dinger equation in $\mathbb{R}^3$

Analysis of PDEs 2025-12-25 v1

Authors: Boyu Jiang , Jiawei Shen , Kexue Li

Abstract

This paper investigates the Cauchy problem for the nonlinear Schr\"odinger equation (NLS) in the mass-supercritical and energy-subcritical regime within three spatial dimensions. For initial data in the critical homogeneous Sobolev space $\dot{H}^{s_c}(\mathbb{R}^3)$ (where $s_c = \frac{5}{6}$ ), we get a uniform decay estimate for the long-time dynamics of solutions, which extends the previous results.

Keywords

nonlinear Schrödinger equation dispersive decay critical Sobolev space mass-supercritical energy-subcritical Cauchy problem uniform decay estimate

Cite

@article{arxiv.2512.20683,
  title  = {Dispersive decay for the Inter-critical nonlinear Schr\"{o}dinger equation in $\mathbb{R}^3$},
  author = {Boyu Jiang and Jiawei Shen and Kexue Li},
  journal= {arXiv preprint arXiv:2512.20683},
  year   = {2025}
}

Comments

arXiv admin note: text overlap with arXiv:2411.01466 by other authors

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