Inverse of divergence and homogenization of compressible Navier-Stokes equations in randomly perforated domains

Abstract

We analyze behavior of weak solutions to compressible fluid flows in a bounded domain in ${\mathbb{R}}^3$, randomly perforated by tiny balls with random size. Assuming the radii of the balls scale like ${\epsilon }^{\alpha }$, $\alpha >3$, with $\epsilon$ denoting the average distance between the balls, the problem homogenize with the same limiting equation. Our main contribution is a construction of the Bogovski\uı operator, uniformly in $\epsilon$, without any assumptions on the minimal distance between the balls.

Corrected moment bound assumption on the radii

Cited by in corpus (2)

• Homogenization and low Mach number limit of compressible Navier-Stokes equations in critically perforated domains
• Homogenization of the full compressible Navier-Stokes-Fourier system in randomly perforated domains