Speaker: Professor Emmanuel Trelat，Sorbonne Université

Inviter: 阮国兴 副研究员

Title: From microscopic to macroscopic scale equations: mean field, hydrodynamic and graph limits

Language: English

Time & Venue: 2024.12.13  09:30-10:30  S813

Abstract: Considering finite particle systems, we elaborate on various ways to pass to the limit as the number of agents tends to infinity, either by mean field limit, deriving the Vlasov equation, or by hydrodynamic or graph limit, obtaining the Euler equation. We provide convergence estimates. We also show how to pass from Liouville to Vlasov or to Euler by taking adequate moments. Our results encompass and generalize a number of known results of the literature.As a surprising consequence of our analysis, we show that sufficiently regular solutions of any quasilinear PDE can be approximated by solutions of systems of N particles, to within 1/log(log(N)).This is a work with Thierry Paul.