Homogenization of the two-dimensional evolutionary compressible Navier-Stokes equations

TL;DR

This paper studies how solutions to 2D compressible Navier-Stokes equations behave in perforated domains with tiny holes, showing convergence to solutions in the non-perforated domain.

Contribution

It demonstrates the homogenization of the 2D compressible Navier-Stokes equations in perforated domains with very small holes, establishing convergence results.

Findings

Density and velocity converge to non-perforated domain solutions

Homogenization holds in the subcritical case of tiny holes

Provides rigorous mathematical proof of convergence

Abstract

We consider the evolutionary compressible Navier-Stokes equations in a two-dimensional perforated domain, and show that in the subcritical case of very tiny holes, the density and velocity converge to a solution of the evolutionary compressible Navier-Stokes equations in the non-perforated domain.