  We study the long time behaviour of the kinetic Fokker-Planck equation with
mean field interaction, whose limit is often called Vlasov-Fkker-Planck
equation. We prove a uniform (in the number of particles) exponential
convergence to equilibrium for the solutions in the weighted Sobolev space H 1
($\mu$) with a rate of convergence which is explicitly computable and
independent of the number of particles. The originality of the proof relies on
functional inequalities and hypocoercivity with Lyapunov type conditions,
usually not suitable to provide adimensional results.
