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We study the energy conservation for the weak solutions to the compressiblePrimitive Equations (CPE) system with degenerate viscosity. We give sufficientconditions on the regularity of weak solutions for the energy equality to hold,even for solutions that may include a vacuum. In this paper, we give twotheorems, the first one gives regularity in the classical isotropic Sobolev andBesov spaces. The second one state result in anisotropic spaces. We get newregularity results in the second theorem because of the special structure ofthe CPE system, which is in contrast to compressible Navier-Stokes equations.

Energy equality for the compressible Primitive Equations with vacuum