Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential

Zuyu Ma; Yilin Song; Kai Yang; Xiaoyi Zhang

doi:10.48550/arxiv.2604.15362

Back

Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential

Preprint

Open access

Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential

Zuyu Ma, Yilin Song, Kai Yang and Xiaoyi Zhang

ArXiv.org

Cornell University

04/13/2026

DOI: 10.48550/arxiv.2604.15362

Files and links (1)

url

https://doi.org/10.48550/arxiv.2604.15362View

Preprint (Author's original) This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

We study the threshold scattering problem for the energy-critical nonlinear Schrödinger equation with a repulsive inverse-square potential(a/(|x|²)) > 0in dimensionsd= 4, 5, 6 . On the energy level surface determined by the ground state of the energy-critical NLS without potential, we show that, despite the absence of a ground state in this setting, a strong form of rigidity persists below the kinetic threshold. Specifically, we prove that any solution on this energy surface with kinetic energy strictly below that of the ground state is global and scatters to zero. Our approach combines refined modulation analysis, a center-translated global Virial estimate, and a bootstrap argument to control the modulation parameters.

Mathematics - Analysis of PDEs

Details

Title: Subtitle: Threshold Scattering for the Energy-Critical NLS with a Repulsive Inverse Square Potential
Creators: Zuyu Ma
Yilin Song
Kai Yang
Xiaoyi Zhang
Resource Type: Preprint
Publication Details: ArXiv.org
DOI: 10.48550/arxiv.2604.15362
ISSN: 2331-8422
Publisher: Cornell University; Ithaca, New York
Language: English
Date posted: 04/13/2026
Academic Unit: Mathematics
Record Identifier: 9985154890702771

Metrics

1 Record Views