Calculus of Variations and Geometric Measure Theory

F. Lagoutière - F. Santambrogio - S. Tran Tien

Vanishing viscosity limit for aggregation-diffusion equations

created by santambro on 14 Mar 2023
modified on 04 Jul 2024



Inserted: 14 mar 2023
Last Updated: 4 jul 2024

Year: 2023


This article is devoted to the convergence analysis of the diffusive approximation of the measure-valued solutions to the so-called aggregation equation, which is now widely used to model collective motion of a population directed by an interaction potential. We prove, over the whole space in any dimension, a uniform-in-time convergence in Wasserstein distance, in the general framework of Lipschitz potentials, and provide a $O(\sqrt{\varepsilon})$ rate, where $\varepsilon$ is the diffusion parameter, when the potential is $\lambda-$convex. We give an extension to some repulsive potentials and prove sharp convergence rates of the steady states towards the Dirac mass, under some uniform attractiveness assumptions.