In this paper, we justify the low Mach number limit of the steady irrotational Euler flows for the airfoil problem, which is the first result for the low Mach number limit of the steady Euler flows in an exterior domain. The uniform estimates on the compressibility parameter \(\varepsilon \), which is singular for the flows, are established via a variational approach based on the compressible–incompressible difference functions. The limit is on the Hölder space and is unique. Moreover, the convergence rate is of order \(\varepsilon ^2\). It is noticeable that, due to the feature of the airfoil problem, the extra force dominates the asymptotic decay rate of the compressible flow to the infinity. And the effect of extra force vanishes in the limiting process from compressible flows to the incompressible ones, as the Mach number goes to zero.

在本文中，我们为翼型问题证明了恒定非旋转欧拉流的低马赫数极限，这是在外部域中稳定欧拉流动的低马赫数极限的第一个结果。对于可压缩性参数\（\ varepsilon \），对于流动是唯一的，可以通过基于可压缩-不可压缩差分函数的变分方法建立统一估计。极限在Hölder空间上是唯一的。此外，收敛速度约为\（\ varepsilon ^ 2 \）。值得注意的是，由于翼型问题的特征，额外的力主导了可压缩流至无穷大的渐近衰减率。随着马赫数变为零，在从可压缩流到不可压缩流的限制过程中，多余力的作用消失了。