The kinetic Fokker-Planck equation with mean field interaction

DOI10.1016/j.matpur.2021.04.001zbMath1480.60235arXiv1912.02594OpenAlexW3146063833MaRDI QIDQ2027553

Wei Liu, Chaoen Zhang, Arnaud Guillin, Li-ming Wu

Publication date: 27 May 2021

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02594

zbMATH Keywords

logarithmic Sobolev inequalityPoincaré inequalitieshypocoercivitymean field interactionLyapunov conditions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Diffusion processes (60J60) Fokker-Planck equations (35Q84)

Related Items (11)

Uniform long-time and propagation of chaos estimates for mean field kinetic particles in non-convex landscapes ⋮ Large and moderate deviation principles for McKean-Vlasov SDEs with jumps ⋮ Exponential entropy dissipation for weakly self-consistent Vlasov-Fokker-Planck equations ⋮ Scaling limit of moderately interacting particle systems with singular interaction and environmental noise ⋮ Path dependent McKean-Vlasov SDEs with Hölder continuous diffusion ⋮ Asymptotic behaviors of small perturbation for multivalued Mckean-Vlasov stochastic differential equations ⋮ Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics ⋮ Coupling by reflection for controlled diffusion processes: turnpike property and large time behavior of Hamilton-Jacobi-Bellman equations ⋮ Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models ⋮ Convergence rates for the Vlasov-Fokker-Planck equation and uniform in time propagation of chaos in non convex cases ⋮ Entropic turnpike estimates for the kinetic Schrödinger problem

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