Inverse of Divergence and Homogenization of Compressible Navier-Stokes Equations in Randomly Perforated Domains

We analyze the behavior of weak solutions to compressible viscous fluid flows in a bounded domain in 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 to the same limiting equation. Our main contribution is a construction of the Bogovski(SIC) operator, uniformly in epsilon, without any assumptions on the minimal distance between the balls.

Automated summary

This article analyzes the behavior of weak solutions to compressible viscous fluid flows in a bounded domain randomly perforated by tiny balls with random size. Assuming a relationship between the radii of the balls and the average distance between them, the problem homogenizes to the same limiting equation. The main contribution of this article is the construction of the Bogovski (SIC) operator regarding the balls, uniformly in epsilon, without any assumptions on the minimal distance between the balls.