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arXiv · 2602.21344

Scattering map for the Vlasov--Poisson system with a repulsive harmonic potential

Wenrui Huang·Hyunwoo Kwon
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Abstract

We consider the Vlasov--Poisson system with a repulsive harmonic potential and prove the (modified) scattering of solutions, as well as the existence of wave operators, in any spatial dimension $d\geq 2$. The main novelty of this work is the construction of the wave operators and the introduction of the lens transform for the Vlasov--Poisson system. In addition, we provide a new and simpler proof that relaxes the assumptions on the initial data compared with those in Bigorgne, Velozo Ruiz, and Velozo Ruiz (2025) and Velozo Ruiz, and Velozo Ruiz (2024).

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Wenrui Huang, Hyunwoo Kwon. 2026-02-24. Scattering map for the Vlasov--Poisson system with a repulsive harmonic potential. https://arxiv.org/abs/2602.21344

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