粘性导热流体相对论动力学中全波数模的衰减和次发光
Decay and Subluminality of Modes of all Wave Numbers in the Relativistic Dynamics of Viscous and Heat Conductive Fluids
摘要：
为了进一步证实二阶双曲偏微分方程组的因果关系和稳定性，该方程组模拟了具有粘性和热传导的正压流体的相对论动力学（H。Freistühler和B. Temple，J. Math. Phys. 59（2018）），本文研究了该系统的Fourier-Laplace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。对于非正压流体的相关模型也显示了稳定性（H。Freistühler和B.寺程序R. A 470（2014）和Proc. R. A 473（2017））。尽管从数值证据的意义上来说，这些性质已经知道了一段时间，但这里给出的任意坐标系中任意波数模式的次发光性的完全分析证明似乎是关于耗散相对论性流体动力学的任何五场公式的第一个。
英文摘要：
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 (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 (2014) and Proc. R. Soc. A 473 (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 five-field formulation of dissipative relativistic fluid dynamics.
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