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arXiv · 2412.13434

The Vlasov-Poisson system with a perfectly conducting wall: Convex domains

Wenrui Huang·Benoît Pausader·Masahiro Suzuki
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Abstract

We consider the Vlasov--Poisson system in a $C^3$ convex domain $D$ with a perfectly conducting wall. We introduce the asymptotic domain $D_{\infty}$ for the domain $D$. Then under acceptable assumptions on $D$, we show that for localized initial data, the velocity of particles is asymptotically supported in the (closure of the) asymptotic domain $\overline{D_{\infty}}$ and the solutions exhibit the asymptotics of modified scattering.

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Wenrui Huang, Benoît Pausader, Masahiro Suzuki. 2024-12-18. The Vlasov-Poisson system with a perfectly conducting wall: Convex domains. https://arxiv.org/abs/2412.13434

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