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We prove the existence of a contraction rate for Vlasov-Fokker-Planckequation in Wasserstein distance, provided the interaction potential is(locally) Lipschitz continuous and the confining potential is both Lipschitzcontinuous and greater than a quadratic function, thus requiring no convexityconditions. Our strategy relies on coupling methods suggested by A. Eberleadapted to the kinetic setting enabling also to obtain uniform in timepropagation of chaos in a non convex setting.

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