The invariant group transformations of three-dimensional hydrodynamic equations derived from the Boltzmann equation are studied. Three levels (with respect to the Knudsen number) of hydrodynamic description are considered and compared: (a) Euler equations, (b) Navier-Stokes equations, (c) Generalized Burnett equations (GBEs), which replace the original (ill-posed) Burnett equations. The main attention is paid to group analysis of GBEs in their most general formulation because this and related questions have not been studied before in the literature. The results of group analysis of GBEs and, for comparison, of similar results for Euler and Navier-Stokes equations are presented in two theorems and discussed in detail. It is remarkable that the use of computer code greatly simplifies the proof of the results for GBEs, which are very cumbersome equations with many undetermined parameters.

中文翻译：

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稀有气体流体力学方程组的对称性

研究了从玻耳兹曼方程导出的三维流体动力学方程的不变群变换。考虑并比较了三个层次的水力描述（相对于Knudsen数）：（a）欧拉方程，（b）Navier-Stokes方程，（c）通用Burnett方程（GBE），它们代替了原始的（不适定的） ）伯内特方程。主要关注以最笼统的形式对GBE进行分组分析，因为以前没有在文献中研究过此问题和相关问题。GBE的组分析结果，以及作为比较的Euler和Navier-Stokes方程的相似结果，在两个定理中给出并进行了详细讨论。值得注意的是，计算机代码的使用大大简化了GBE结果的证明，