相对论动力学色散关系：相对论Bhatnagar-Gross-Krook模型和Grad 14矩展开的比较
The relativistic kinetic dispersion relation: Comparison of the relativistic Bhatnagar-Gross-Krook model and Grad's 14-moment expansion
摘要：
本文研究了Marle和Anderson-Witting模型的线性化动力学方程的Cauchy问题，并与14矩理论作了比较。首先，我们提出了一个修改的Marle模型，以提高所得的输运系数，符合由完整的玻尔兹曼方程。利用改进的Marle模型和Anderson-Witting模型，我们计算了在BGK近似的有效性范围内动力学正确的色散关系。与非因果的一阶Chapman-Enskog近似相比，包含耗散电流时间导数的14阶矩理论具有因果结构。然而，14矩理论的色散关系并不能准确地描述动力学方程的结果。因此，我们的计算表明，保持这些二阶项并不简单地对应于改善相对论流体力学的物理描述。
英文摘要：
In this paper, we study the Cauchy problem of the linearized kinetic equations for the models of Marle and Anderson-Witting, and compare these dispersion relations with the 14-moment theory. First, we propose a modification of the Marle model to improve the resultant transport coefficients in accord with those obtained by the full Boltzmann equation. Using the modified Marle model and Anderson-Witting model, we calculate dispersion relations that are kinetically correct within the validity of the BGK approximation. The 14-moment theory that includes the time derivative of dissipation currents has causal structure, in contrast to the acausal first-order Chapman-Enskog approximation. However, the dispersion relation of the 14-moment theory does not accurately describe the result of the kinetic equation. Thus, our calculation indicates that keeping these second-order terms does not simply correspond to improving the physical description of the relativistic hydrodynamics.
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