Particles approximations of Vlasov equations with singular forces : Part. 2

Maxime Hauray (1) , Pierre-Emmanuel Jabin (2, 3)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 TOSCA - Simuler et calibrer des modèles stochastiques
3 JAD - Laboratoire Jean Alexandre Dieudonné

We prove propagation of chaos for a system of particles interacting with a singular interaction force of the type $1/|x|^\alpha$, with $\alpha <1$ in dimension $d \geq 3$. We also recover the usual results, with sharper propagation of chaos, for forces with large enough cut-off that are valid for $\alpha < d-1$, i.e. almost up to the most interesting case of Coulombian or gravitationnal interaction.

Mots clés: Derivation of kinetic equations. Particle methods. Vlasov equation. Propagation of chaos; Derivation of kinetic equations. Particle methods. Vlasov equation. Propagation of chaos.

Domaines: Equations aux dérivées partielles [math.AP]

Maxime Hauray, Pierre-Emmanuel Jabin. Particles approximations of Vlasov equations with singular forces : Part. 2. 2011. ⟨hal-00609453v2⟩