Ad hoc test functions for homogenization of compressible viscous fluid with application to the obstacle problem in dimension two

TL;DR

This paper introduces specialized test functions to enhance the analysis of homogenization for viscous compressible fluids in perforated domains, demonstrating that small obstacles do not affect fluid dynamics in two dimensions.

Contribution

It develops ad hoc test functions that improve homogenization results and applies them to show small obstacles do not impact fluid behavior in 2D.

Findings

Improved homogenization results in 2D and 3D

Small obstacles do not influence fluid dynamics in 2D

Enhanced analytical tools for fluid homogenization

Abstract

In this paper we highlight a set of ad hoc test functions to study the homogenization of viscous compressible fluid in domains with tiny holes. This set of functions allows to improve previous results in dimensions two and three. As an application we show that the presence of a small obstacle does not influence the dynamics of a viscous compressible fluid in dimension two.