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Asymptotic behavior of the one-dimensional Vlasov--Poisson system with a repulsive harmonic potential

  • Wenrui Huang
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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.

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Cite

BibTeXRIS
BibTeX
@misc{huang2026asymptotic,
  title = {{Asymptotic behavior of the one-dimensional Vlasov--Poisson system with a repulsive harmonic potential}},
  author = {Wenrui Huang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.02551},
  eprint = {2610.02551},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.02551},
}
RIS
TY  - UNPB
TI  - Asymptotic behavior of the one-dimensional Vlasov--Poisson system with a repulsive harmonic potential
AU  - Wenrui Huang
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.02551
UR  - https://arxiv.org/abs/2610.02551
AB  - 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.
ER  -