THE KINETIC FOKKER-PLANCK EQUATION WITH GENERAL FORCE

Chuqi Cao (1, 2)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL

We consider the kinetic Fokker-Planck equation with a class of general force. We prove the existence and uniqueness of a positive normalized equilibrium (in the case of a general force) and establish some exponential rate of convergence to the equilibrium (and the rate can be explicitly computed). Our results improve similar results established by [26, 5, 6, 14, 10, 11, 1] to general force case, and improve the non-quantitative rate of convergence in [18] to quantitative explicit rate.

Domaines: Equations aux dérivées partielles [math.AP]

Chuqi Cao. THE KINETIC FOKKER-PLANCK EQUATION WITH GENERAL FORCE. 2019. ⟨hal-02127815v1⟩