An optimal transport approach of hypocoercivity for the 1d kinetic Fokker-Plank equation

Samir Salem

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arXiv · 2102.10667

An optimal transport approach of hypocoercivity for the 1d kinetic Fokker-Plank equation

Samir Salem

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Abstract

A quadratic optimal transport metric on the set of probability measure over $\R^2$ is introduced. The quadratic cost is given by the euclidean norm on $\R^2$ associated to some well chosen symmetric positive matrix, which makes the metric equivalent to the usual Wasserstein-2 metric. The dissipation of the distance to the equilibrium along the kinetic Fokker-Planck flow, is bounded by below in terms of the distance itself. It enables to obtain some new type of trend to equilibrium estimate in Wasserstein-2 like metric, in the case of non-convex confinement potential.

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Samir Salem. 2021-02-21. An optimal transport approach of hypocoercivity for the 1d kinetic Fokker-Plank equation. https://arxiv.org/abs/2102.10667

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