Freistühler Heinrich, Temple Blake
Department of Mathematics, University of Konstanz, 78457 Konstanz, Germany.
Department of Mathematics, University of California, Davis, CA 95616, USA.
Proc Math Phys Eng Sci. 2017 May;473(2201):20160729. doi: 10.1098/rspa.2016.0729. Epub 2017 May 24.
We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navier-Stokes equations.
通过要求相对论耗散张量与相对论欧拉方程相结合，能构成一个二阶偏微分方程组，当用使欧拉方程在一阶意义下为对称双曲型的自然戈东诺夫变量来书写时，该方程组在二阶意义下是对称双曲型的，我们推导出了一类广义相对论耗散张量。我们证明，这类张量包含一个唯一元素，它代表相对论耗散流体动力学的一种因果表述，该表述（i）在粘性系数和热传导系数的一阶近似下等同于埃卡特和朗道的经典描述，并且（ii）其信号速度被光速严格限制。基于这些性质，我们提出这个方程组作为经典纳维 - 斯托克斯方程相对论对应物的自然候选者。
