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

2024/12/18 by Huang, Wenrui, Pausader, Benoît, Suzuki, Masahiro · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.13434

Abstract

We consider the Vlasov--Poisson system in a C³ convex domain D with a perfectly conducting wall. We introduce the asymptotic domain D_∞ 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 D_∞ and the solutions exhibit the asymptotics of modified scattering.

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