Singular limit for the compressible Navier--Stokes equations with the hard sphere pressure law on expanding domains

TL;DR

This paper studies the asymptotic behavior of the compressible Navier-Stokes equations with a hard-sphere pressure law on expanding domains, proving convergence to the incompressible Euler system under specific conditions.

Contribution

It establishes the singular limit of the compressible Navier-Stokes system with a hard-sphere pressure law on expanding domains, including convergence rates and conditions.

Findings

Convergence to the incompressible Euler system on R^3.

Rate of convergence expressed in terms of characteristic numbers.

Conditions ensuring acoustic waves do not reach the boundary during expansion.

Abstract

The article is devoted to the asymptotic limit of the compressible Navier-Stokes system with a pressure obeying a hard--sphere equation of state on a domain expanding to the whole physical space $R^3$. Under the assumptions that acoustic waves generated in the case of ill-prepared data do not reach the boundary of the expanding domain in the given time interval and a certain relation between the Reynolds and Mach numbers and the radius of the expanding domain, we prove that the target system is the incompressible Euler system on $R^3$. We also provide an estimate of the rate of convergence expressed in terms of characteristic numbers and the radius of domains.