Existence result for stationary compressible fluids and asymptotic behavior in thin films

TL;DR

This paper investigates the existence and behavior of stationary compressible fluids with density-dependent viscosities, establishing well-posedness and applying results to thin film flows to justify simplified models.

Contribution

It provides new existence results for stationary compressible Navier-Stokes equations with variable viscosities and extends these findings to thin domain applications, validating the compressible Reynolds equations.

Findings

Proved well-posedness of compressible Navier-Stokes with density-dependent viscosities.

Established asymptotic behavior in thin film regimes.

Justified the use of compressible Reynolds equations in thin domains.

Abstract

In this paper, we are first interested in the compressible Navier-Stokes equations with densitydependent viscosities in bounded domains with on-homogeneous Dirichlet conditions. We study the wellposedness of such models with non-constant coefficients in non-stationary and stationary cases. We apply the last result in thin domains context, justifying the compressible Reynolds equations.