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arXiv · 2410.17978

On the stability of vacuum in the screened Vlasov-Poisson equation

Mikaela Iacobelli·Stefano Rossi·Klaus Widmayer
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Abstract

We study the asymptotic behavior of small data solutions to the screened Vlasov-Poisson equation on $\mathbb{R}^d\times\mathbb{R}^d$ near vacuum. We show that for dimensions $d\geq 2$, under mild assumptions on localization (in terms of spatial moments) and regularity (in terms of at most three Sobolev derivatives) solutions scatter freely. In dimension $d=1$, we obtain a long time existence result in analytic regularity.

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Mikaela Iacobelli, Stefano Rossi, Klaus Widmayer. 2024-10-23. On the stability of vacuum in the screened Vlasov-Poisson equation. https://arxiv.org/abs/2410.17978

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