In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number limit, which is the first result of the low Mach number limit on the steady Euler flows. We establish several uniform estimates, which does not depend on the Mach number, to validate the convergence of the compressible flow with extra force to the corresponding incompressible flow, which is free from the extra force effect, as the Mach number goes to zero. The limit is on the Holder space and is unique. Moreover, the convergence rate is of order $\varepsilon^2$, which is higher than the ones in the previous results on the low Mach number limit for the unsteady flow.

中文翻译：

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多维喷嘴中稳定欧拉流的低马赫数限制

在本文中，我们考虑多维喷嘴中的稳定无旋欧拉流。提供了关于不可压缩流的存在性和唯一性的第一个严格证明。然后，我们证明相应的低马赫数限制是正确的，这是稳定欧拉流的低马赫数限制的第一个结果。我们建立了几个不依赖于马赫数的统一估计，以验证具有额外力的可压缩流收敛到相应的不可压缩流，当马赫数变为零时，该不可压缩流不受额外力的影响。限制在 Holder 空间上并且是唯一的。此外，收敛速度为 $\varepsilon^2$，高于之前的非定常流低马赫数限制结果中的收敛速度。