2024/05/12 by Noemi David, Alpár R. Mészáros, David, Noemi +3 · 1 citation
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #Quantum, superfluid, helium dynamics #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2405.07227
openalex publication_date 2024/05/12 · openalex created_date 2024/05/15 · openalex updated_date 2026/07/28
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.