Derivation of the inviscid compressible primitive equations. (English) Zbl 1524.35479
Summary: Primitive Equations (PE) are an important model which is widely used in the geophysical research and the mathematical analysis. In the previous results, people derive PE from the Navier-Stokes or the Euler system by an asymptotic analysis or a numerical approximation. Here, we give a rigorous mathematical derivation of inviscid compressible Primitive Equations from the Euler system in a periodic channel, utilizing the relative entropy inequality.
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q30 | Navier-Stokes equations |
| 86A05 | Hydrology, hydrography, oceanography |
| 86A10 | Meteorology and atmospheric physics |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
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