From the Relativistic Mixture of Gases to the Relativistic Cucker–Smale Flocking
From the Relativistic Mixture of Gases to the Relativistic Cucker–Smale Flocking
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DOI：
10.1007/s00205-019-01452-y
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发表时间：
2019-10
影响因子：
2.5
通讯作者：
Seung‐Yeal Ha;Jeongho Kim;T. Ruggeri
中科院分区：
文献类型：
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作者：
Seung‐Yeal Ha;Jeongho Kim;T. Ruggeri
本文提出了一个多温欧拉气体混合物的相对论模型。对于所提出的相对论模型，我们明确地确定产生的条款通过熵原理的成分之间的能量-动量的交换。我们在经典环境中使用气体混合物的均匀解和热机械Cucker-Smale（简称TCS）植绒模型的类比（Ha和Ruggeri in Arch Ration Mech Anal 223：1397-1425，2017）来推导TCS模型的相对论对应物。此外，我们还利用aprinNR子系统理论导出了相对论Cucker-Smale（简称CS）模型。对于导出的相对论CS模型，我们提供了一个充分的框架，导致指数群集的通信权重，也表明，相对论CS模型减少到经典的CS模型，光速趋于无穷大，在任何有限的时间间隔。
We present a relativistic model for a mixture of Euler gases with multiple temperatures. For the proposed relativistic model, we explicitly determine production terms resulting from the interchange of energy–momentum between the constituents via the entropy principle. We use the analogy with the homogeneous solutions of a mixture of gases and the thermomechanical Cucker–Smale (in short TCS) flocking model in a classical setting (Ha and Ruggeri in Arch Ration Mech Anal 223:1397–1425, 2017) to derive a relativistic counterpart of the TCS model. Moreover, we employ the theory of aprincipal subsystemto derive the relativistic Cucker–Smale (in short CS) model. For the derived relativistic CS model, we provide a sufficient framework leading to the exponential flocking in terms of communication weights and also show that the relativistic CS model reduces to the classical CS model, as the speed of light tends to infinity in any finite-time interval.