A Vlasov-Poisson plasma of infinite mass with a point charge

Gang Li; Xianwen Zhang

doi:10.3934/krm.2018015

Article Contents

2018, Volume 11, Issue 2: 303-336. Doi: 10.3934/krm.2018015

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A Vlasov-Poisson plasma of infinite mass with a point charge

Gang Li and
Xianwen Zhang^,

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China

* Corresponding author: Xianwen Zhang
* Corresponding author: Xianwen Zhang

Received: February 28, 2017

Published: March 2018

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Abstract

We study the time evolution of the three dimensional Vlasov-Poisson plasma interacting with a positive point charge in the case of infinite mass. We prove the existence and uniqueness of the classical solution to the system by assuming that the initial density slightly decays in space, but not integrable. This result extends a previous theorem for Yukawa potential obtained in [10] to the case of Coulomb interaction.

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Mathematics Subject Classification: Primary: 82D10, 35Q83, 76X05; Secondary: 35L60.

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