Mean-field limits: from particle descriptions to macroscopic equations

Abstract

We rigorously derive pressureless Euler-type equations with nonlocal dissipative terms in velocity and aggregation equations with nonlocal velocity fields from Newton-type particle descriptions of swarming models with alignment interactions. We crucially make use of a discrete version of a modulated kinetic energy together with the bounded Lipschitz distance for measures in order to control terms in its time derivative due to the nonlocal interactions.

References in corpus (2)

• State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
• Next Order Asymptotics and Renormalized Energy for Riesz Interactions

Cited by in corpus (2)

• Learning Anisotropic Interaction Rules from Individual Trajectories in a Heterogeneous Cellular Population
• Derivation of Euler's equations of perfect fluids from von Neumann's equation with magnetic field