Homogenization of the evolutionary compressible Navier-Stokes-Fourier system in domains with tiny holes

Abstract

We study the homogenization of the evolutionary compressible Navier--Stokes--Fourier system in a bounded three-dimensional domain perforated with a large number of very tiny holes. We show that under suitable assumptions on the smallness and distribution of the holes the limit system remains the same in the unperforated domain.

One of the main novelty in the paper consists in the treatment of the entropy inequality and thus the paper also improves the related result in the steady case from the paper by Y. Lu and M.

Pokorny.

Keywords

• Homogenization
• Evolutionary compressible Navier–Stokes–Fourier system
• Entropy inequality