THE KINETIC FOKKER-PLANCK EQUATION WITH WEAK CONFINEMENT FORCE

Chuqi Cao (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We consider the kinetic Fokker-Planck equation with weak confinement force. We proved some (polynomial and sub-exponential) rate of convergence to the equilibrium (depending on the space to which the initial datum belongs). Our results generalized the result in [4, 5, 21, 11, 10, 9, 1, 14] to weak confinement case.

Mots clés: weak hypocoercivity; weak hypodissipativity; Fokker-Planck equation; semigroup; weak Poincaré inequality; rate of convergence

Domaines: Equations aux dérivées partielles [math.AP]

Chuqi Cao. THE KINETIC FOKKER-PLANCK EQUATION WITH WEAK CONFINEMENT FORCE. 2018. ⟨hal-01697058v2⟩