Communications in Mathematical Sciences

Volume 17 (2019)

Number 8

The kinetic Fokker–Planck equation with weak confinement force

Pages: 2281 – 2308



Chuqi Cao (Centre de Recherche en Mathématiques de la Décision (CEREMADE), Université Paris-Dauphine, Paris, France)


We consider the kinetic Fokker–Planck equation with weak confinement force. We prove some (polynomial and sub-exponential) rate of convergence to the equilibrium (depending on the space to which the initial datum belongs). Our results generalize some results known for strong confinement to the weak confinement case.


weak hypocoercivity, weak hypodissipativity, Fokker–Planck equation, semigroup, weak Poincaré inequality, rate of convergence

2010 Mathematics Subject Classification

35B40, 35P15, 35Q84, 47D06

This work was supported by grants from Région Ile-de-France towards the DIM program.

Received 7 June 2018

Accepted 3 September 2019

Published 3 February 2020