On the local uniqueness of steady states for the Vlasov-Poisson system

Motivated by recent results of Lemou-M\'ehats-R\"aphael and Lemou concerning the quatitative stability of some suitable steady states for the Vlasov-Poisson system, we investigate the local uniqueness of steady states near these one. This research is inspired by analogous results of Couffrut and \v{S}ver\'ak in the context of the 2D Euler equations

Global strong solutions in R3 for ionic Vlasov-Poisson systems

Systems of Vlasov-Poisson type are kinetic models describing dilute plasma. The structure of the model differs according to whether it describes the electrons or positively charged ions in the plasma. In contrast to the electron case, where the well-posedness theory for Vlasov-Poisson systems is well established, the well-posedness theory for ion models has been investigated more recently. In this article, we prove global well-posedness for two Vlasov-Poisson systems for ions, posed on the whole three-dimensional Euclidean space R3, under minimal assumptions on the initial data and the confining potential

Singular Limits for Plasmas with Thermalised Electrons

This work is concerned with the study of singular limits for the Vlasov-Poisson system in the case of massless electrons (VPME), which is a kinetic system modelling the ions in a plasma. Our objective is threefold: first, we provide a mean field derivation of the VPME system in dimensions from a system of N extended charges. Secondly, we prove a rigorous quasineutral limit for initial data that are perturbations of analytic data, deriving the Kinetic Isothermal Euler (KIE) system from the VPME system in dimensions . Lastly, we combine these two singular limits in order to show how to obtain the KIE system from an underlying particle system.This work was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) grant EP/L016516/1 for the University of Cambridge Centre for Doctoral Training, the Cambridge Centre for Analysis; and the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 726386)