三维气体动力学欧拉方程组的群分析
Group analysis of three dimensional Euler equations of gas dynamics
摘要：
本文考虑三维理想多方气体非定常流动的控制方程。该系统的基本相似性约简。得到了与对称性有关的简化方程和精确解。这个结果被用来给出系统对时空$\RR^4$的伽利略运动的不变性。然后，给出了一维子代数的对称代数的最优系统。
英文摘要：
In this paper, the equations governing the unsteady flow of a perfect polytropic gas in three space dimensions are considered. The basic similarity reductions for this system are performed. Reduced equations and exact solutions associated with the symmetries are obtained. This results is used to give the invariance of system up to Galilean motions of space-times $\RR^4$. Then, an optimal system of one-dimensional sub-algebras for symmetry algebra of this system is given.
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