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We provide an estimation of the dissipation of the Wasserstein 2 distancebetween the law of some interacting $N$-particle system, and the $N$ timestensorized product of solution to the corresponding limit nonlinearconservation law. It then enables to recover classical propagation of chaosresults in the case of Lipschitz coefficients, uniform in time propagation ofchaos in the case of strictly convex coefficients. But also some recent resultsas the case of particle in a double well potential.

A gradient flow approach of uniform in time propagation of chaos for particles in double a well confinement