On the low Mach number limit of compressible flows in exterior moving domains

TL;DR

This paper investigates the transition from compressible to incompressible fluid flow in exterior moving domains, employing spectral analysis and the RAGE theorem to establish the limit behavior of solutions.

Contribution

It introduces a novel approach using spectral analysis and the RAGE theorem to rigorously prove the low Mach number limit in exterior moving domains.

Findings

Established dispersion of acoustic waves via spectral analysis.

Proved convergence of compressible solutions to incompressible Navier-Stokes solutions.

Extended the understanding of low Mach number limits in dynamic exterior domains.

Abstract

We study the incompressible limit of solutions to the compressible barotropic Navier-Stokes system in the exterior of a bounded domain undergoing a simple translation. The problem is reformulated using a change of coordinates to fixed exterior domain. Using the spectral analysis of the wave propagator, the dispersion of acoustic waves is proved by the means of the RAGE theorem. The solution to the incompressible Navier-Stokes equations is identified as a limit.