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The kinetic Fokker-Planck equation with general force

Cao, Chuqi (2021), The kinetic Fokker-Planck equation with general force, Journal of Evolution Equations, 21, p. 2293–2337. 10.1007/s00028-021-00684-4

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Journal of Evolution Equations
Volume
21
Publisher
Springer
Published in
Paris
Pages
2293–2337
Publication identifier
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Author(s)
Cao, Chuqi
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
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.
Subjects / Keywords
kinetic Fokker-Planck equation