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We study an asymptotic limit of Vlasov type equation with nonlocal interaction forces where the friction terms are dominant. We provide a quantitative estimate of this large friction limit from the kinetic equation to a continuity type equation with a nonlocal velocity field, the so-called aggregation equation, by employing 2-Wasserstein distance. By introducing an intermediate system, given by the pressureless Euler equations with nonlocal forces, we can quantify the error between the spatial densities of the kinetic equation and the pressureless Euler system by means of relative entropy type arguments combined with the 2-Wasserstein distance. This together with the quantitative error estimate between the pressureless Euler system and the aggregation equation in 2-Wasserstein distance in [Commun. Math. Phys, 365, (2019), 329–361] establishes the quantitative bounds on the error between the kinetic equation and the aggregation equation.
Keywords: Large friction limit, Relative entropy, Pressureless Euler system, Wasserstein distance, Aggregation equation, Kinetic swarming models
Carrillo, José A. 1 ; Choi, Young-Pil 2
@article{AIHPC_2020__37_4_925_0,
author = {Carrillo, Jos\'e A. and Choi, Young-Pil},
title = {Quantitative error estimates for the large friction limit of {Vlasov} equation with nonlocal forces},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {925--954},
publisher = {Elsevier},
volume = {37},
number = {4},
year = {2020},
doi = {10.1016/j.anihpc.2020.02.001},
mrnumber = {4104830},
zbl = {1440.35322},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.02.001/}
}
TY - JOUR AU - Carrillo, José A. AU - Choi, Young-Pil TI - Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2020 SP - 925 EP - 954 VL - 37 IS - 4 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.02.001/ DO - 10.1016/j.anihpc.2020.02.001 LA - en ID - AIHPC_2020__37_4_925_0 ER -
%0 Journal Article %A Carrillo, José A. %A Choi, Young-Pil %T Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces %J Annales de l'I.H.P. Analyse non linéaire %D 2020 %P 925-954 %V 37 %N 4 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2020.02.001/ %R 10.1016/j.anihpc.2020.02.001 %G en %F AIHPC_2020__37_4_925_0
Carrillo, José A.; Choi, Young-Pil. Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces. Annales de l'I.H.P. Analyse non linéaire, Tome 37 (2020) no. 4, pp. 925-954. doi: 10.1016/j.anihpc.2020.02.001
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