We show that the Reynolds defect measure for a dissipative weak solution of the compressible Euler system vanishes for large time. This may be seen as a piece of evidence that the dissipative solutions are asymptotically close to weak solutions in the turbulent regime, whence suitable for describing compressible fluid flows in the long run.

中文翻译：

---

关于Euler系统耗散解的长期行为的说明

我们表明，可压缩的欧拉系统的耗散弱解的雷诺缺陷测度在很大程度上消失了。这可以看作是一条证据，表明耗散解在湍流状态下渐近接近于弱解，从长远来看，它适合于描述可压缩流体的流动。