The two dimensional Vlasov-Poisson system with steady spatial asymptotics

Zili Chen; Xiuting Li; Xianwen Zhang

doi:10.3934/krm.2017039

Article Contents

2017, Volume 10, Issue 4: 977-1009. Doi: 10.3934/krm.2017039

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The two dimensional Vlasov-Poisson system with steady spatial asymptotics

a.
Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi 330031, China
b.
School of Automation, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China
c.
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China

* Corresponding author: Zili Chen
* Corresponding author: Zili Chen

Received: March 31, 2015

Revised: October 31, 2016

Published: November 2017

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Abstract

We consider a two dimensional collisionless plasma interacting with a fixed background of positive charge, the density of which depends only upon velocity variable $v$ and decays as $|v| \to \infty $. Suppose that mobile negative ions balance the positive charge as spatial variable $|x|\to \infty $, then on the mesoscopic level the system is characterized by the two dimensional Vlasov-Poisson system with steady spatial asymptotics, whose total positive charge and total negative charge are both infinite. Smooth solutions with appropriate asymptotic behavior are shown to exist locally in time, and an "almost optimal" criterion for the continuation of these solutions is established.

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Mathematics Subject Classification: Primary: 35F20, 35J05; Secondary: 82D10.

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