Hypocoercivity in Wasserstein-1 for the kinetic Fokker-Planck equation via Malliavin Calculus

2018/10/02 by Josephine Evans, Evans, Josephine · 1 citation
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Gas Dynamics and Kinetic Theory #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Electrodynamics and Casimir Effect

paper · pdf · doi:10.48550/arxiv.1810.01324

openalex publication_date 2018/10/02 · openalex created_date 2018/10/12 · openalex updated_date 2026/07/28

Abstract

We study the kinetic Fokker-Planck equation on the whole space with a confining potential. We show quantitative rates of exponential convergence to equilibrium in a well chosen Wasserstein-1 distance. We use the Wasserstein-1 version of Harris's theorem introduced by Hairer and Mattingly. We make use of similarities between hypocoercivity and hypoellipticity in order to use Malliavin calculus to see hypocoercivity for this equation on the level of the SDE.

Citations

• Isotropic Hypoellipticity and Trend to Equilibrium for the Fokker-Planck Equation with a High-Degree Potential
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus

Cited by

• The Kinetic Fokker-planck Equation With Mean Field Interaction

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