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

We consider the homogenization of the compressible Navier-Stokes-Fourier equations in a randomly perforated domain in $${\mathbb {R}}^3$$ R 3 . Assuming that the particle size scales like $$\varepsilon ^\alpha $$ ε α , where $$\varepsilon >0$$ ε > 0 is their mutual distance and $$\alpha >3$$ α > 3 , we show that in the limit $$\varepsilon \rightarrow 0$$ ε → 0 , the velocity, density, and temperature converge to a solution of the same system. We follow the methods of Lu and Pokorný [https://doi.org/10.1016/j.jde.2020.10.032] and Pokorný and Skříšovský [https://doi.org/10.1007/s41808-021-00124-x] where they considered the full system in periodically perforated domains.

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