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

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

2010-02-26

arxiv.org/abs/1002.4926v1

Math. Meth. Appl. Sci. 30: 529-548, 2007

Mathematics

Analysis of PDEs

17 pages, no figures

Scientific paper

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.

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