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

2024/10/23 by Mikaela Iacobelli, Stefano Rossi, Iacobelli, Mikaela +3 · 1 citation
Engineering · Mathematics · #35B35 #35B40 #35F20 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Material Science and Thermodynamics #Mathematical Physics (math-ph) #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2410.17978

openalex publication_date 2024/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of small data solutions to the screened Vlasov–Poisson equation on near vacuum. We show that for dimensions , 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 , we obtain a long‐time existence result in analytic regularity.

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