Rigorous justification of hydrostatic approximation of compressible fluid flow equations

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Résumé

In this paper, we obtain the 3D compressible primitive equations approximation with gravity by taking the small aspect ratio limit to the Navier-Stokes equations. We use the versatile relative entropy inequality to prove rigorously the limit from the compressible Navier-Stokes equations with a pressure law of the form p(ρ) = ρ^2 to the compressible primitive equations.

Mots-clés

anisotropic Navier-Stokes equations, aspect ratio limit, compressible primitive equations, relative entropy