Homogenization problems for the compressible Navier-Stokes system in 2D perforated domains

TL;DR

This paper investigates the homogenization of the stationary compressible Navier-Stokes equations in a 2D domain with tiny perforations, showing that the effective equations remain unchanged in the limit.

Contribution

First to analyze homogenization of the compressible Navier-Stokes system in 2D perforated domains, demonstrating the limit system is unaffected by the perforations.

Findings

Homogenization does not alter the fluid motion in the limit.

The same system of equations is obtained asymptotically.

First such result for 2D compressible case.

Abstract

In this paper, we study the homogenization problems for the stationary compressible Navier-Stokes system in a bounded 2D domain, where the domain is perforated with very tiny holes (or obstacles) whose diameters are much smaller than their mutual distances. We obtain that the process of homogenization doesn't change the motion of the fluids. From another point of view, we obtain the same system of equations in the asymptotic limit. It is the first result of homogenization problem in the compressible case in 2 dimensions.