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Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold
Abstract
We consider the focusing cubic nonlinear Schrodinger equation with a repulsive inverse-power potential V(x)=a|x|−μ, where a>0 and 1<μ≤ 2. At the mass-energy threshold, Miao, Murphy, and Zheng, as well as Ardila, Hamano, and Ikeda, established sharp scattering results in the positive virial region. In this paper, we continue to study the dynamics in the negative virial region and show that, in each time direction, solutions either blow up in finite time or grow up.
Related
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- Bilinear estimates for Schrödinger equation with repulsive inverse-square potential and its application
- Normalized ground states and a mass-constrained scattering threshold for the inhomogeneous NLS with an inverse-square potential
- Strong and Weak-Type Dispersive Estimates for the Energy-Critical Nonlinear Schrödinger Equation with an Inverse-Square Potential
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BibTeX
@misc{ardila2026blowup,
title = {{Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold}},
author = {Alex H. Ardila and Zuyu Ma and Ying Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.13750},
eprint = {2609.13750},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.13750},
}
RIS
TY - UNPB
TI - Blow-up or grow-up for the focusing 3D cubic NLS with a repulsive inverse-power potential at the mass--energy threshold
AU - Alex H. Ardila
AU - Zuyu Ma
AU - Ying Wang
PY - 2026
DA - 2026/09/12
PB - arXiv
DO - 10.48550/arxiv.2609.13750
UR - https://arxiv.org/abs/2609.13750
AB - We consider the focusing cubic nonlinear Schrodinger equation with a repulsive inverse-power potential V(x)=a|x|^−μ, where a>0 and 1<μ≤ 2. At the mass-energy threshold, Miao, Murphy, and Zheng, as well as Ardila, Hamano, and Ikeda, established sharp scattering results in the positive virial region. In this paper, we continue to study the dynamics in the negative virial region and show that, in each time direction, solutions either blow up in finite time or grow up.
ER -