On the hydrostatic approximation of compressible anisotropic Navier–Stokes equations

In this work, we obtain the hydrostatic approximation by taking small aspect ratio limit to Navier–Stokes equations. The (the of depth horizontal width) is a geometrical constraint in general large scale motions meaning that vertical significantly smaller than horizontal. We use versatile relative entropy inequality prove rigorously from compressible equations Primitive Equations. This first work for proving and derive