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Anelastic approximation as a singular limit of the compressible Navier-Stokes system. (English) Zbl 1146.35073

In this article, the authors study the behavior of weak solutions of the compressible Navier-Stokes system (NSS) in a slab geometry, in the regime when both the Mach and Froude numbers are proportional to a small parameter \(\varepsilon >0\). They prove the convergence of solutions of (NSS) to those of a limit system, the so-called anelastic approximation, describing a flow for which the limit density depends on the vertical coordinate.

MSC:

35Q30 Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
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