Mean-Field Limits: From Particle Descriptions to Macroscopic Equations
José A. Carrillo, Young-Pil Choi
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. Crucially, we 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.
Topics & Concepts
Dissipative systemLipschitz continuityBounded functionClassical mechanicsPhysicsParticle systemMathematical analysisMathematicsComplex systemNonlinear systemKinetic energyTime derivativeUniform boundednessStatistical physicsBoundary value problemAttractorParticle (ecology)Order (exchange)Vector fieldParticle velocityDissipationField equationMinificationTotal energyMathematical Biology Tumor GrowthGas Dynamics and Kinetic TheoryMicro and Nano Robotics