Homogenization of stationary Navier--Stokes--Fourier system in domains with tiny holes

TL;DR

This paper investigates how the stationary Navier--Stokes--Fourier system behaves in a domain with many tiny holes, showing that under certain conditions, the system's limit remains unchanged in the perforated domain.

Contribution

It demonstrates that the homogenized limit of the stationary Navier--Stokes--Fourier system is unaffected by tiny holes under specific assumptions, extending understanding of fluid behavior in perforated domains.

Findings

Homogenized system remains unchanged despite tiny holes.

Conditions on hole size and distribution are crucial.

Results apply to three-dimensional perforated domains.

Abstract

We study the homogenization of stationary compressible Navier--Stokes--Fourier system in a bounded three dimensional domain perforated with a large number of very tiny holes. Under suitable assumptions imposed on the smallness and distribution of the holes, we show that the homogenized limit system remains the same in the domain without holes.