Weak Solutions for the Vlasov-Poisson Initial-Boundary Value Problem with Bounded Electric Field

Abstract

The aim of this work is to construct weak solutions for the three dimensional Vlasov-Poisson initial-boundary value problem with bounded electric field. The main ingredient consists of estimating the change in momentum along characteristics of regular electric fields inside bounded spatial domains. As direct consequences, the propagation of the momentum moments and the existence of weak solution satisfying the balance of totalenergy are obtained.

Keywords

Vlasov-Poisson equations / Vlasov-Maxwell equations / Weak solutions / 35F30 / 35L40

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