Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases

@article{Guillin2022ConvergenceRF,
  title={Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases},
  author={Arnaud Guillin and Pierre Le Bris and Pierre Monmarch'e},
  journal={Electronic Journal of Probability},
  year={2022}
}
Abstract We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is (locally) Lipschitz continuous and the confining potential is both Lipschitz continuous and greater than a quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle [Ebe16] adapted to the kinetic setting enabling also to obtain uniform in time propagation of chaos in a non convex… 

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