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

Francesco Fanelli; Ewelina Zatorska

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arXiv · 2107.05157

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

Francesco Fanelli·Ewelina Zatorska

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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.

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Francesco Fanelli, Ewelina Zatorska. 2021-07-12. Low Mach number limit for degenerate Navier-Stokes equations in presence of strong stratification. https://arxiv.org/abs/2107.05157

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