Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces

被引：17

作者：

Carrillo, Jose A. ^{[1
]}

Choi, Young-Pil ^{[2
]}

机构：

[1] Imperial Coll London, Dept Math, London SW7 2AZ, England

[2] Yonsei Univ, Dept Math, Seoul 03722, South Korea

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2020年 / 37卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Large friction limit; Relative entropy; Pressureless Euler system; Wasserstein distance; Aggregation equation; Kinetic swarming models; STRONG RELAXATION LIMIT; EULER;

D O I：

10.1016/j.anihpc.2020.02.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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. (C) 2020 Elsevier Masson SAS. All rights reserved.

引用

页码：925 / 954

页数：30

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