Low Mach number limit for degenerate Navier-Stokes equations in presence of strong stratification

TL;DR

This paper rigorously analyzes the low Mach and Froude number limits of degenerate compressible Navier-Stokes equations under strong stratification, showing convergence to the generalized anelastic approximation in 3D periodic domains.

Contribution

It provides a rigorous mathematical justification for the convergence to the anelastic approximation in the presence of density-dependent viscosity and singular pressure laws.

Findings

Convergence to the generalized anelastic model is established.

Results hold for ill-prepared initial data.

Analysis covers degenerate viscosity and singular pressure near vacuum.

Abstract

In this paper, we investigate the low Mach and low Froude numbers limit for the compressible Navier-Stokes equations with degenerate, density-dependent, viscosity coefficient, in the strong stratification regime. We consider the case of a general pressure law with singular component close to vacuum, and general ill-prepared initial data. We perform our study in the three-dimensional periodic domain. We rigorously justify the convergence to the generalised anelastic approximation, which is used extensively to model atmospheric flows.