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
TypeDocument de travail / Working paper
Series titleCahier de recherche CEREMADE, Université Paris Dauphine-PSL
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (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 / KeywordsOrnstein-Uhlenbeck equation; time average; local equilibria; Lions' lemma; Poincaré inequalities; hypocoercivity
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