To further confirm the causality and stability of a second-order hyperbolic system of partial differential equations that models the relativistic dynamics of barotropic fluids with viscosity and heat conduction [H. Freistühler and B. Temple, J. Math. Phys. 59, 063101 (2018)], this paper studies the Fourier–Laplace modes of this system and shows that all such modes, relative to arbitrary Lorentz frames, (a) decay with increasing time and (b) travel at subluminal speeds. Stability is also shown for the related model of non-barotropic fluids [H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014) and H. Freistühler and B. Temple, Proc. R. Soc. A 473, 20160729 (2017)]. Even though these properties had been known for a while in the sense of numerical evidence, the fully analytical proofs for the subluminality of modes of arbitrary wave numbers in arbitrary frames given here appear to be the first regarding any four-field formulation of dissipative relativistic fluid dynamics.

中文翻译：

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粘性和导热流体的相对论动力学中所有波数模式的衰减和亚光度

为了进一步确认偏微分方程的二阶双曲系统的因果关系和稳定性，该系统模拟具有粘度和热传导的正压流体的相对论动力学 [H. Freistühler 和 B. Temple，J. Math。物理。59 , 063101 (2018)]，这篇论文研究了该系统的傅里叶-拉普拉斯模式，并表明所有这些模式，相对于任意洛伦兹框架，（a）随着时间的增加而衰减，（b）以亚光速传播。非正压流体的相关模型也显示了稳定性 [H. Freistühler 和 B. Temple，Proc。R. Soc。A 470 , 20140055 (2014) 和 H. Freistühler 和 B. Temple, Proc. R. Soc。一个473, 20160729 (2017)]。尽管这些性质在数值证据的意义上已经为人所知，但这里给出的任意帧中任意波数模式的亚光度的完全解析证明似乎是关于耗散相对论流体的任何四场公式的第一个证明动力学。