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 (13)

• State Transitions and the Continuum Limit for a 2D Interacting, Self-Propelled Particle System
• The derivation of Swarming models: Mean-Field Limit and Wasserstein distances
• On the Dynamics of Large Particle Systems in the Mean Field Limit
• Quantitative estimate of propagation of chaos for stochastic systems with $W^{-1,\infty }$ kernels
• Mean Field Limit for Coulomb-Type Flows
• Next Order Asymptotics and Renormalized Energy for Riesz Interactions
• Propagation of chaos for the 2D viscous vortex model
• Relative entropy in diffusive relaxation
• From gas dynamics with large friction to gradient flows describing diffusion theories
• Singular Cucker-Smale Dynamics
• First-order aggregation models and zero inertia limits
• First-order aggregation models with alignment
• Convergence to Equilibrium in Wasserstein distance for damped Euler equations with interaction forces

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