Anelastic approximation as a singular limit of the compressible Navier-Stokes system

Abstract

Considering compressible Navier-Stokes system in a slab geometry in the regime when both Mach and Froude numbers vanish at the same rate, we study the behavior of corresponding weak solutions, that are known to exist glbally-in-time (for large data). We establish their convergence to a solution of the so-called anelastic approximation when the limit flow is stratified, i.e., the limit density depends effectively on the vertical coordinate.

Keywords

• Anelastic
• approximation
• singular
• limit
• compressible
• Navier-Stokes
• system