Homogenization of the full compressible Navier-Stokes-Fourier system in randomly perforated domains

TL;DR

This paper studies the homogenization of the full compressible Navier-Stokes-Fourier system in randomly perforated domains, showing convergence of solutions as the perforations become small and dense.

Contribution

It extends previous periodic domain results to randomly perforated domains, demonstrating homogenization for the full system under specific scaling assumptions.

Findings

Velocity, density, and temperature converge to solutions of the same system in the limit

Established homogenization results for randomly perforated domains

Extended methods from periodic to random perforation settings

Abstract

We consider the homogenization of the compressible Navier-Stokes-Fourier equations in a randomly perforated domain in $\mathbb{R}^3$. Assuming that the particle size scales like $\varepsilon^\alpha$, where $\varepsilon>0$ is their mutual distance and $\alpha>3$, we show that in the limit $\varepsilon\to 0$, the velocity, density, and temperature converge to a solution of the same system. We follow the methods of Lu and Pokorn\'{y} [https://doi.org/10.1016/j.jde.2020.10.032], where they considered the full system in periodically perforated domains.