We show that the Euler system of gas dynamics in ${\mathbb{R}}^d$, $d=2,3$, with positive far field density and arbitrary far field entropy, admits infinitely many steady solutions with compactly supported velocity. The same proof yields a similar result for the incompressible Euler system with variable density. In particular, these are examples of global in time smooth (non-trivial) solutions for the corresponding time-dependent systems.

中文翻译：

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关于欧拉系统稳态解的几点看法。 ${\mathbb{[R}}^d$

我们证明了欧拉气体动力学系统 ${\mathbb{[R}}^d$， $d=2，3$具有正的远场密度和任意远场熵的，可以无穷多个稳定的速度支持稳定的解。对于具有可变密度的不可压缩的欧拉系统，相同的证明得出相似的结果。尤其是，这些是相应时间相关系统的全局时间平滑（非平凡）解决方案的示例。