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

### José A. Carrillo

Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom### Young-Pil Choi

Department of Mathematics, Yonsei University, Seoul 03722, Republic of Korea

## Abstract

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.

## Cite this article

José A. Carrillo, Young-Pil Choi, Quantitative error estimates for the large friction limit of Vlasov equation with nonlocal forces. Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 4, pp. 925–954

DOI 10.1016/J.ANIHPC.2020.02.001