Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems

This note adapts a probabilistic approach to establish a quantified estimate of the overdamped limit for the Vlasov–Fokker–Planck equation towards the aggregation–diffusion equation, which in particular includes cases of the Newtonian type singular forces. The proofs are based on the investigation o...

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Autor principal:	Hui Huang
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Overdamped Large friction Zero inertia Tightness Applied mathematics. Quantitative methods T57-57.97
Acceso en línea:	https://doaj.org/article/f85d183a8d9e47e482ddeb9a2e0e194e
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spelling	oai:doaj.org-article:f85d183a8d9e47e482ddeb9a2e0e194e2021-11-18T04:52:40ZQuantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems2666-818110.1016/j.padiff.2021.100186https://doaj.org/article/f85d183a8d9e47e482ddeb9a2e0e194e2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666818121000978https://doaj.org/toc/2666-8181This note adapts a probabilistic approach to establish a quantified estimate of the overdamped limit for the Vlasov–Fokker–Planck equation towards the aggregation–diffusion equation, which in particular includes cases of the Newtonian type singular forces. The proofs are based on the investigation of the weak convergence of the corresponding stochastic differential equations (SDEs) of Mckean type in the continuous path space. We show that one can recover the same (actually stronger) overdamped limit result as in Choi and Tse (2020) under the same assumptions.Hui HuangElsevierarticleOverdampedLarge frictionZero inertiaTightnessApplied mathematics. Quantitative methodsT57-57.97ENPartial Differential Equations in Applied Mathematics, Vol 4, Iss , Pp 100186- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Overdamped Large friction Zero inertia Tightness Applied mathematics. Quantitative methods T57-57.97
spellingShingle	Overdamped Large friction Zero inertia Tightness Applied mathematics. Quantitative methods T57-57.97 Hui Huang Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems
description	This note adapts a probabilistic approach to establish a quantified estimate of the overdamped limit for the Vlasov–Fokker–Planck equation towards the aggregation–diffusion equation, which in particular includes cases of the Newtonian type singular forces. The proofs are based on the investigation of the weak convergence of the corresponding stochastic differential equations (SDEs) of Mckean type in the continuous path space. We show that one can recover the same (actually stronger) overdamped limit result as in Choi and Tse (2020) under the same assumptions.
format	article
author	Hui Huang
author_facet	Hui Huang
author_sort	Hui Huang
title	Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems
title_short	Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems
title_full	Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems
title_fullStr	Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems
title_full_unstemmed	Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems
title_sort	quantitative estimate of the overdamped limit for the vlasov–fokker–planck systems
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/f85d183a8d9e47e482ddeb9a2e0e194e
work_keys_str_mv	AT huihuang quantitativeestimateoftheoverdampedlimitforthevlasovfokkerplancksystems
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Quantitative estimate of the overdamped limit for the Vlasov–Fokker–Planck systems

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