Time averages for kinetic Fokker-Planck equations
Brigati, Giovanni (2022), Time averages for kinetic Fokker-Planck equations. https://basepub.dauphine.psl.eu/handle/123456789/23606
View/ Open
Type
Document de travail / Working paperDate
2022Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSLPublished in
Paris
Pages
18
Metadata
Show full item recordAbstract (EN)
We consider kinetic Fokker-Planck (or Vlasov-Fokker-Planck) equations on the torus with Maxwellian or fat tail local equilibria. Results based on weak norms have recently been achieved by S. Armstrong and J.-C. Mourrat in case of Maxwellian local equilibria. Using adapted Poincaré and Lions-type inequalities, we develop an explicit and constructive method for estimating the decay rate of time averages of norms of the solutions, which covers various regimes corresponding to subexponential, exponential and superexponential (including Maxwellian) local equilibria. As a consequence, we also derive hypocoercivity estimates, which are compared to similar results obtained by other techniques.Subjects / Keywords
Ornstein-Uhlenbeck equation; time average; local equilibria; Lions' lemma; Poincaré inequalities; hypocoercivityRelated items
Showing items related by title and author.
-
Dolbeault, Jean; Li, Xingyu (2018) Article accepté pour publication ou publié
-
Cao, Chuqi (2019-10-10) Thèse
-
Bouin, Emeric; Dolbeault, Jean; Ziviani, Luca (2023) Document de travail / Working paper
-
Mischler, Stéphane; Mouhot, Clément (2016) Article accepté pour publication ou publié
-
Cao, Chuqi (2021) Article accepté pour publication ou publié