This work concerns the zero Mach number limit of the compressible primitive equations. The primitive equations with the incompressibility condition are identified as the limiting equations. The convergence with well-prepared initial data (i.e., initial data without acoustic oscillations) is rigorously justified, and the convergence rate is shown to be of order $$ \mathcal {O}(\varepsilon ) $$ O ( ε ) , as $$ \varepsilon \rightarrow 0^+ $$ ε → 0 + , where $$ \varepsilon $$ ε represents the Mach number. As a byproduct, we construct a class of global solutions to the compressible primitive equations, which are close to the incompressible flows.

中文翻译：

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可压缩原始方程的零马赫数极限：精心准备的初始数据

这项工作涉及可压缩原始方程的零马赫数限制。具有不可压缩条件的原始方程被识别为极限方程。与准备好的初始数据（即没有声学振荡的初始数据）的收敛是严格证明的，并且收敛速度显示为阶 $$ \mathcal {O}(\varepsilon ) $$ O ( ε ) ，如$$ \varepsilon \rightarrow 0^+ $$ ε → 0 + ，其中 $$ \varepsilon $$ ε 代表马赫数。作为副产品，我们构造了一类接近不可压缩流动的可压缩原始方程的全局解。