The gyrokinetic limit for the two dimensional Vlasov-Poisson system with multi-point charges

Fuente: arXiv
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Main Author: Wu, Jingpeng
Format: Preprint
Published: 2023
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author Wu, Jingpeng
author_facet Wu, Jingpeng
contents In this article, we investigate the gyrokinetic limit for the two dimensional Vlasov-Poisson system with multi-point charges. We show that the solution converges to a measure-valued solution of the Euler equation with a defect measure, which extends the results of Miot (Nonlinearity 32(2):654-677, 2019) to the case of multi-point charges and removes the smallness condition $\sup_{0<\varepsilon<1}\|f_{\varepsilon}^0\|_{L^1}<1$. The main difficulty arises from the fact that the orbits of point charges will intersect frequently and rapidly as the magnetic field intensity becomes large. To overcome the problem, we adopt the techniques recently developed by Wu and Zhang (Journal of Statistical Physics 190:183, 2023) combined with a new technique introduced here.
format Preprint
id arxiv_https___arxiv_org_abs_2307_13442
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The gyrokinetic limit for the two dimensional Vlasov-Poisson system with multi-point charges
Wu, Jingpeng
Analysis of PDEs
35Q83, 82D10, 35B40, 35A24
In this article, we investigate the gyrokinetic limit for the two dimensional Vlasov-Poisson system with multi-point charges. We show that the solution converges to a measure-valued solution of the Euler equation with a defect measure, which extends the results of Miot (Nonlinearity 32(2):654-677, 2019) to the case of multi-point charges and removes the smallness condition $\sup_{0<\varepsilon<1}\|f_{\varepsilon}^0\|_{L^1}<1$. The main difficulty arises from the fact that the orbits of point charges will intersect frequently and rapidly as the magnetic field intensity becomes large. To overcome the problem, we adopt the techniques recently developed by Wu and Zhang (Journal of Statistical Physics 190:183, 2023) combined with a new technique introduced here.
title The gyrokinetic limit for the two dimensional Vlasov-Poisson system with multi-point charges
topic Analysis of PDEs
35Q83, 82D10, 35B40, 35A24
url https://arxiv.org/abs/2307.13442