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

Abstract

We prove the existence of a contraction rate for Vlasov-Fokker-Planck equation in Wasserstein distance, provided the interaction potential is Lipschitz continuous and the confining potential is both (locally) Lipschitz continuous and greater than a quadratic function, thus requiring no convexity conditions. Our strategy relies on coupling methods suggested by A. Eberle [22] adapted to the kinetic setting enabling also to obtain uniform in time propagation of chaos in a non convex setting.