SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 795-812, January 2021.
This paper is concerned with the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De Lellis and Székelyhidi and by Chiodaroli enable us to prove failure of uniqueness on a finite time-interval for admissible solutions starting from any continuously differentiable initial density and suitably constructed bounded initial momenta. In particular, this extends Chiodaroli's work from periodic boundary conditions to bounded domains or the whole space.

中文翻译：

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具有紧支撑空间的可压缩Euler方程的非唯一容许弱解。

SIAM数学分析期刊，第53卷，第1期，第795-812页，2021年1月。
本文涉及等熵可压缩Euler方程的Cauchy问题的紧密支持的容许解的存在。在一个以上的空间维度中，De Lellis和Székelyhidi以及Chiodaroli所开发的凸积分技术使我们能够在有限的时间间隔内证明唯一性的失败，这是从任何可连续微分的初始密度和适当构造的有界初始动量开始的可接受解的。特别是，这将Chiodaroli的工作从周期性边界条件扩展到有界域或整个空间。