Propagation of chaos for the VPFP equation with a polynomial cut-off

Abstract

We consider a $N$-particle system interacting through the Newtonian potential with a polynomial cut-off in the presence of noise in velocity. We rigorously prove the propagation of chaos for this interacting stochastic particle system. Taking the cut-off like $N^{-\delta }$ with $\delta <1/d$ in the force, we provide a quantitative error estimate between the empirical measure associated to that $N$-particle system and the solutions of the $d$-dimensional Vlasov-Poisson-Fokker-Planck system. We also study the propagation of chaos for the Vlasov-Fokker-Planck equation with less singular interaction forces than the Newtonian one.

References in corpus (6)

• A well-posedness theory in measures for some kinetic models of collective motion
• The derivation of Swarming models: Mean-Field Limit and Wasserstein distances
• On Kac's Chaos And Related Problems
• Propagation of chaos for the 2D viscous vortex model
• Propagation of chaos for Hölder continuous interaction kernels via Glivenko-Cantelli
• Propagation of chaos for some 2 dimensional fractional Keller Segel equations in diffusion dominated and fair competition cases

Cited by in corpus (13)

• Mean Field Limit for Coulomb-Type Flows
• Propagation of chaos: a review of models, methods and applications. II. Applications
• Propagation of chaos for the Keller-Segel equation over bounded domains
• Geometric ergodicity of Langevin dynamics with Coulomb interactions
• A new approach to the mean-field limit of Vlasov-Fokker-Planck equations
• A new perspective on Wasserstein distances for kinetic problems
• On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
• Stability estimates for magnetized Vlasov equations
• Fractional Keller-Segel Equation: Global Well-posedness and Finite Time Blow-up
• On well-posedness and singularity formation for the Euler-Riesz system
• Global weak solutions to the Vlasov-Poisson-Fokker-Planck-Navier-Stokes system
• Quantitative estimate of the overdamped limit for the Vlasov-Fokker-Planck systems
• Particles approximation for some 1D kinetic Fokker-Planck equations with singular forces