Quantitative homogenization of the compressible Navier-Stokes equations towards Darcy's law

2024/03/19 by Richard M. Höfer, Šárka Nečasová, Höfer, Richard M. +3
Chemical Engineering · Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Composite Material Mechanics #FOS: Mathematics #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2403.12616

openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

We consider the solutions ρ_ε, u_ε to the compressible Navier-Stokes equations (NSE) in a domain periodically perforated by holes of diameter ε>0. We focus on the case where the diameter of the holes is of the same order as the distance between neighboring holes. This is the same setting investigated in the paper by Masmoudi [\urlhttp://www.numdam.org/article/COCV₂002_₈_₈85₀.pdf], where convergence ρ_ε, u_ε of the system to the porous medium equation has been shown. We prove a quantitative version of this convergence result provided that the solution of the limiting system is sufficiently regular. The proof builds on the relative energy inequality satisfied by the compressible NSE.

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