Scattering of the Vlasov–Riesz System in the Three Dimensions

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发表日期：

2026年7月22日

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Wenrui Huang,
Hyunwoo Kwon

摘要

We consider an asymptotic behavior of solutions to the Vlasov–Riesz system of order $\alpha $ $α$ in $\mathbb {R}^3$ $R^{3}$ which is a kinetic model induced by Riesz interactions. We prove small data scattering when $1/2<\alpha <1$ $1 / 2 < α < 1$ and modified scattering when $1<\alpha <1+\delta $ $1 < α < 1 + δ$ for some $\delta >0$ $δ > 0$ . Moreover, we show the existence of (modified) wave operators for such a regime. To the best of our knowledge, this is the first result on the existence of modified scattering with polynomial correction in kinetic models.