An anelastic approximation arising in astrophysics

TL;DR

This paper derives an anelastic approximation from the compressible Navier-Stokes equations in astrophysics, demonstrating convergence under specific low Mach and Froude number regimes using advanced Strichartz estimates.

Contribution

It establishes a rigorous asymptotic limit of the compressible Navier-Stokes system to an anelastic model in an astrophysical context, employing novel frequency localized estimates.

Findings

Convergence of the compressible system to an anelastic approximation.

Application of Strichartz estimates to acoustic equations.

Validation of the approximation for ill-prepared initial data.

Abstract

We identify the asymptotic limit of the compressible non-isentropic Navier-Stokes system in the regime of low Mach, low Froude and high Reynolds number. The system is driven by a long range gravitational potential. We show convergence to an anelastic system for ill-prepared initial data. The proof is based on frequency localized Strichartz estimates for the acoustic equation based on the recent work of Metcalfe and Tataru.