Calculus of Variations and Geometric Measure Theory

N. David - A. R. Mészáros - F. Santambrogio

Improved convergence rates for the Hele-Shaw limit in the presence of confining potentials

created by mészáros on 15 May 2024

[BibTeX]

Preprint

Inserted: 15 may 2024
Last Updated: 15 may 2024

Year: 2024

ArXiv: 2405.07227 PDF

Abstract:

Nowadays a vast literature is available on the Hele-Shaw or incompressible limit for nonlinear degenerate diffusion equations. This problem has attracted a lot of attention due to its applications to tissue growth and crowd motion modelling as it constitutes a way to link soft congestion (or compressible) models to hard congestion (or incompressible) descriptions. In this paper, we address the question of estimating the rate of this asymptotics in the presence of external drifts. In particular, we provide improved results in the 2-Wasserstein distance which are global in time thanks to the contractivity property that holds for strictly convex potentials.