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arXiv · 2510.11901

Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations

Nicolò Forcillo·Alessio Porretta
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Abstract

We prove long-time contractivity estimates and exponential rates of convergence to equilibrium for solutions of hypoelliptic diffusion equations, which include the well-known Kolmogorov equation and similar kinetic Fokker-Planck equations in $\R^d$. Compared to the existing literature, our proof exploits a different approach, elementary and self-contained, based on oscillation estimates for the adjoint problem. We first prove contractivity in Wasserstein distances through doubling variables (coupling) methods. Next, we upgrade the estimate to weighted $L^1$-(or total variation) norms, thanks to short-time hypocoercivity gradient estimates.

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Nicolò Forcillo, Alessio Porretta. 2025-10-13. Long-time contractivity estimates for kinetic Kolmogorov-Fokker-Planck equations. https://arxiv.org/abs/2510.11901

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