Asymptotic behavior of the one-dimensional Vlasov--Poisson system with a repulsive harmonic potential
Year: 2026
Type: preprint
Abstract: We study the one-dimensional Vlasov--Poisson system with a repulsive harmonic potential. For repulsive self-interactions, we prove modified scattering for initial data of arbitrary size, assuming only velocity weights and one derivative; no smallness, symmetry, compact support, or spatial moments are required. In the lens variables of \cite{HK26}, the self-consistent force carries a nonintegrable time weight. We remove it by a momentum correction that solves a forced Burgers equation; the repulsive sign makes this correction monotone, which gives bounds for large data. We also construct modified wave operators for both signs of the interaction. Together with \cite{VR24,BVR25,HK26}, this gives a scattering theory in every dimension.
Source: arXiv (Cornell University)
Author: Huang, Wenrui
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220403450