Low Mach Number Limit for the Degenerate Navier–Stokes Equations in Presence of Strong Stratification

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.