论文标题
关于$ \ mathbb {r}^d $中欧拉系统稳定解决方案的一些评论
Some remarks on steady solutions to the Euler system in $\mathbb{R}^d$
论文作者
论文摘要
我们表明，$ \ Mathbb {r}^d $，$ d = 2,3 $中的气体动力学系统的欧拉系统，具有正面的远处密度和任意的远场熵，以紧凑的速度承认许多稳定的解决方案。相同的证明对于具有可变密度的不可压缩欧拉系统产生了相似的结果。特别是，这些是全局时间的示例，用于相应的时间依赖性系统的平滑（非平凡）解决方案。
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.
