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arXiv · 1506.06173

Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus

Helge Dietert·Josephine Evans·Thomas Holding
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Abstract

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.

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Helge Dietert, Josephine Evans, Thomas Holding. 2015-06-19. Convergence to equilibrium for the kinetic Fokker-Planck equation on the torus. https://doi.org/10.3934/krm.2018056

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