Communications in Mathematical Sciences
Volume 17 (2019)
The kinetic Fokker–Planck equation with weak confinement force
Pages: 2281 – 2308
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