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

Abstract

We consider the Vlasov--Poisson system with a repulsive harmonic potential and prove (modified) scattering of solutions for small initial data. Moreover, we construct (modified) wave operators for small final data. The main novelty of this work is to introduce the kinetic lens transform which enables us to relax the regularity assumption and the spatial decay assumption on the initial data compared to Bigorgne, Velozo Ruiz, and Velozo Ruiz (2025) and Velozo Ruiz, and Velozo Ruiz (2024)and to construct wave operators.

arXiv comment27 pages; v2. fixed typos and gaps in the construction of wave operators