Abstract
In this paper, we investigate the incompressible limit of the compressible primitive equations with the effect of gravity. First we prove that the estimates of the local strong solutions to the compressible primitive equations with γ=2 are uniform to the Mach number. Then we show that the local strong solutions of the system with well-prepared initial data, as well as their time derivatives, converge to those of the inhomogeneous incompressible primitive equations as the Mach number tends to zero. The convergence rates are shown to be identical to the Mach number.
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