4h-minicourse at the VIASM Summer School in Mathematical Physics 2024 in Huế, Vietnam
Abstract:
One major open problem in mathematical physics still concerns the justification of the Vlasov-Poisson equation as the mean-field limit for systems of classical particles with Coulomb interactions. In this course, we shall review this classical problem, describe some previous approaches, and present a new dual hierarchical method that was recently developed with D. Bresch and P.-E. Jabin. If time allows, we shall also discuss related questions regarding correlation estimates and corrections to mean field.
Slides:
Lecture 1: Introduction to classical mean field
Lecture 2: How the mean-field problem is easier for inertialess particles
Lectures 3-4: Dual hierarchical approach