  We study convergence to equilibrium for the kinetic Fokker-Planck equation on
the torus. Solving the stochastic differential equation, we show exponential
convergence in the Monge-Kantorovich-Wasserstein $\mathcal{W}_2$ distance.
Finally, we investigate if such a coupling can be obtained by a co-adapted
coupling, and show that then the bound must depend on the square root of the
initial distance.
