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

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.