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

Francesco Fanelli (1, 2) , Ewelina Zatorska

1 EDPA - Équations aux dérivées partielles, analyse
2 ICJ - Institut Camille Jordan

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.

Mots clés: compressible Navier-Stokes equations; density-dependent viscosity; low Mach and Froude numbers; strong stratification; cold pressure

Domaines: Equations aux dérivées partielles [math.AP]

Francesco Fanelli, Ewelina Zatorska. Low Mach number limit for degenerate Navier-Stokes equations in presence of strong stratification. Communications in Mathematical Physics, 2023, 400 (3), pp.1463-1506. ⟨10.1007/s00220-022-04624-2⟩. ⟨hal-03286164⟩