Local Existence for the One-dimensional Vlasov-Poisson System with Infinite Mass

TL;DR

This paper proves local-in-time existence of smooth solutions for a one-dimensional Vlasov-Poisson system modeling a collisionless plasma with infinite total charge, and establishes criteria for extending these solutions.

Contribution

It introduces a framework for analyzing the Vlasov-Poisson system with infinite mass, demonstrating local existence and continuation criteria for solutions.

Findings

Existence of smooth solutions with appropriate asymptotics

Criteria for solution continuation

Handling of infinite total charge in the model

Abstract

A collisionless plasma is modeled by the Vlasov-Poisson system in one dimension. We consider the situation in which mobile negative ions balance a fixed background of positive charge, which is independent of space and time, as x tends to positive or negative infinity. Thus, the total positive charge and the total negative charge are both infinite. Smooth solutions with appropriate asymptotic behavior are shown to exist locally in time, and criteria for the continuation of these solutions are established.