当前位置: X-MOL 学术J. Stat. Phys. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Generic instabilities in the relativistic Chapman–Enskog heat conduction law
Journal of Statistical Physics ( IF 1.6 ) Pub Date : 2020-06-08 , DOI: 10.1007/s10955-020-02578-0
Ana L. García-Perciante , Marcelo E. Rubio , Oscar A. Reula

We address the well-posedness of the Cauchy problem corresponding to the relativistic first-order fluid equations, coupled with the Chapman–Enskog heat-flux constitutive relation. We show that the system of equations that results by considering linear perturbations with respect to a generic time direction is non-hyperbolic, since there are modes that may arbitrarily grow as wave-number increases. Then, using a result provided by Strang (J Differ Equ 2:107–114, 1966), we conclude that the full non-linear first-order theory is also non-hyperbolic, thus admitting an ill-posed initial-value formulation. Unlike Eckart’s theory, these instabilities are not present when the time direction is aligned with the fluid’s direction. However, since in general the fluid velocity is not surface-forming, the instability can only be avoided in the particular case where no rotation is present.

中文翻译:

相对论 Chapman-Enskog 热传导定律中的一般不稳定性

我们解决了对应于相对论一阶流体方程的柯西问题的适定性,再加上 Chapman-Enskog 热通量本构关系。我们表明,通过考虑相对于一般时间方向的线性扰动而产生的方程组是非双曲线的,因为存在可能随着波数增加而任意增长的模式。然后,使用 Strang (J Differ Equ 2:107–114, 1966) 提供的结果,我们得出结论,完整的非线性一阶理论也是非双曲的,因此接受不适定的初始值公式。与 Eckart 的理论不同,当时间方向与流体方向一致时,不存在这些不稳定性。然而,由于通常流体速度不是表面形成的,
更新日期:2020-06-08
down
wechat
bug