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From the compressible Navier-Stokes equations to the primitive equations

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TURW05 - Advances in geophysical and astrophysical turbulence

The compressible Navier-Stokes equations with small Mach number, it is classical to approximate the dynamics using the incompressible Navier-Stokes/Boussinesq equations, and rigorous mathematical justification has been available and widely discussed, at least in the case without any boundary. With development of the mathematical theory of the primitive equations, the small aspect ratio limit of the incompressible Navier-Stokes equations has been studied, and rigorous proof has shown the rigidity of the primitive equations as a hydrostatic approximation. We consider the interchange of the aforementioned asymptotic limits, and establish the compressible primitive equations as the intermediate model. It is important to note that, the compressible primitive equations are the starting point of moden weather prediction and climate study, and capture both the acoustic waves due to compressibility and the hydrostatic approximation due to small aspect ratio between vertical and horizontal characteristic scales. Both well-posedness theory and asymptotic limits are investigated for isentropic flows.

This talk is part of the Isaac Newton Institute Seminar Series series.

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