We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent fields, as well as to researches working on broader aspects of relativistic fluid dynamics interested in its mathematical formalism. Instead of complete proofs, which can be found in the published literature, here we focus on the proofs’ main ideas and key concepts. After an introduction to the relativistic Euler equations, we cover the following topics: a new wave-transport formulation of the relativistic Euler equations tailored to applications; the problem of shock formation for relativistic Euler; rough (i.e., low-regularity) solutions to the relativistic Euler equations; the relativistic Euler equations with a physical vacuum boundary; relativistic fluids with viscosity. We finish with a discussion of open problems and future directions of research.

我们回顾了相对论流体数学方面的一些最新进展。目标是为当前感兴趣的一些研究主题提供一个快速的切入点，这些主题可供来自相邻领域的研究生和研究人员访问，以及对相对论流体动力学的数学形式感兴趣的更广泛方面的研究。这里我们关注的不是可以在已发表的文献中找到的完整证明，而是证明的主要思想和关键概念。在介绍了相对论欧拉方程之后，我们涵盖了以下主题：为应用量身定制的相对论欧拉方程的新波传输公式;相对论欧拉的激波形成问题;相对论欧拉方程的粗略（即低规则性）解;具有物理真空边界的相对论欧拉方程;具有粘度的相对论流体。最后，我们讨论了开放性问题和未来的研究方向。