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arXiv · 2407.16919

Scattering of the Vlasov-Riesz system in the three dimensions

Wenrui Huang·Hyunwoo Kwon
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Abstract

We consider an asymptotic behavior of solutions to the Vlasov-Riesz system of order $\alpha$ in $\mathbb{R}^3$ which is a kinetic model induced by Riesz interactions. We prove small data scattering when $1/2<\alpha<1$ and modified scattering when $1<\alpha<1+\delta$ for some $\delta>0$. 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.

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Wenrui Huang, Hyunwoo Kwon. 2024-07-24. Scattering of the Vlasov-Riesz system in the three dimensions. https://arxiv.org/abs/2407.16919

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