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

Thierry Paul (1) , Emmanuel Trélat (2, 3)

1 LYSM - Laboratoire Ypatia des Sciences Mathématiques
2 LJLL (UMR_7598) - Laboratoire Jacques-Louis Lions
3 CaGE - Control And GEometry

Considering deterministic 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.

Mots clés: Agent systems; Mean Field; Hydrodynamic Limit

Domaines: Equations aux dérivées partielles [math.AP]; Systèmes dynamiques [math.DS]; Physique mathématique [math-ph]

Thierry Paul, Emmanuel Trélat. From microscopic to macroscopic scale dynamics: mean field, hydrodynamic and graph limits. 2024. ⟨hal-04577170⟩