On the controllability of the Vlasov-Poisson system in the presence of external force fields

TL;DR

This paper investigates the controllability of Vlasov-Poisson systems with external force fields, extending previous results to include bounded and magnetic forces using local interior control methods.

Contribution

It extends prior work on Vlasov-Poisson controllability by incorporating external force fields such as magnetic and bounded forces.

Findings

Achieved controllability results with external force fields

Extended previous electric field-only results

Demonstrated effectiveness of local interior control methods

Abstract

In this work, we are interested in the controllability of Vlasov-Poisson systems in the presence of an external force field (namely a bounded force field or a magnetic field), by means of a local interior control. We are able to extend the results of [7], where the only present force was the self-consistent electric field.