Mean field limits for charged particles (Q2794847)

This PhD thesis deals with the problem of consistency of microscopic and macroscopic approaches in the kinetic theory of systems with a large number \(N\) of mutually interacting charged particles. In this sense, the author derives the microscopic Vlasov-Poisson's and Vlasov-Maxwell's kinetic equations in the large \(N\) limit, analyzes their solutions in details, and proves the convergence to the corresponding solutions for the mean field approximation typical for the macroscopic approach.NEWLINENEWLINEThe text of the PhD thesis, printed on 9+117 pages, is organized in six chapters: Chapters 1 and 2 introduce the basic concepts of microscopic equations, derivations of the mean field equations, Wasserstein distances, etc. Chapters 3--5 contain the author's original results concerning the mean field limits for a Vlasov-Poisson large \(N\) system without and with extended charge assumption, and a Vlasov-Maxwell large \(N\) system, respectively. Here, one finds rigorous mathematical derivations with proofs and estimates for various physical parameters and processes presented in the considered systems. The final Chapter 8 summarizes the author's new results, discussions, and concluding remarks.