We review the status of mathematical research on the dynamical properties of relativistic fluids in cosmological spacetimes–both, in the presence of gravitational backreaction as well as the evolution on fixed cosmological backgrounds. We focus in particular on the phenomenon of fluid stabilization, which describes the taming effect of spacetime expansion on the fluid. While fluids are in general known to form shocks from regular initial data, spacetime expansion has been found to suppress this behaviour. During the last decade, various rigorous results on this problem have been put forward. We review these results, the mathematical methods involved and provide an outlook on open questions.

中文翻译：

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宇宙时空中的相对论流体


我们回顾了宇宙学时空相对论流体动力学特性的数学研究现状——无论是在引力反作用力存在的情况下，还是在固定宇宙学背景下的演化。我们特别关注流体稳定现象，它描述了时空膨胀对流体的驯服作用。虽然通常已知流体会从常规初始数据中形成激波，但已发现时空膨胀可以抑制这种行为。在过去的十年中，已经提出了关于这个问题的各种严格结果。我们回顾了这些结果、所涉及的数学方法，并提供了对开放性问题的展望。