Shock waves from the inhomogeneous Boltzmann equation
Shock waves from the inhomogeneous Boltzmann equation
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来自非齐次玻尔兹曼方程的冲击波
DOI：
10.1103/physreve.100.062120
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Tran, Minh-Binh
中科院分区：
文献类型：
--
作者：
Pomeau, Yves;Tran, Minh-Binh
我们重新讨论了由玻尔兹曼动力学方程模拟的简单气体中激波的内部结构问题。Pomeau [Y.波莫理论统计16，727（1987）10.1080/00411458708204311]，提出了一种用于由幂律相互作用产生的无限总截面的自相似方法，但是这种自相似形式不具有有限的能量。受Pomeau [Y.波莫理论统计16，727（1987）10.1080/00411458708204311]和Bobylev和Cercignani [A. V. Bobylev和C. Cercignani，J. Stat. 106，1039（2002）10.1023/A：1014037804043]，我们开始了对空间齐次玻尔兹曼方程的解的严格研究，重点是那些不具有有限能量的解。然而，无限能量的解决方案没有物理意义，在目前的框架内的气体动力学理论与碰撞保存总动能。在本工作中，我们对自相似形式进行了修正，以便在能量不再无限并且冲击带来的扰动不会在距离它很远的地方增长的意义上，解在物理上更加合理。在软势情况下，在冷侧。
We revisit the problem on the inner structure of shock waves in simple gases modelized by the Boltzmann kinetic equation. In a paper by Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311], a self-similarity approach was proposed for infinite total cross section resulting from a power-law interaction, but this self-similar form does not have finite energy. Motivated by the work of Pomeau [Y. Pomeau, Transp. Theory Stat. Phys. 16, 727 (1987)10.1080/00411458708204311] and Bobylev and Cercignani [A. V. Bobylev and C. Cercignani, J. Stat. Phys. 106, 1039 (2002)10.1023/A:1014037804043], we started the research on the rigorous study of the solutions of the spatial homogeneous Boltzmann equation, focusing on those which do not have finite energy. However, infinite energy solutions do not have physical meaning in the present framework of kinetic theory of gases with collisions conserving the total kinetic energy. In the present work, we provide a correction to the self-similar form, so that the solutions are more physically sound in the sense that the energy is no longer infinite and that the perturbation brought by the shock does not grow at large distances of it on the cold side in the soft potential case.