双组分混合物的相容动力学模型及其在等离子体中的应用
A consistent kinetic model for a two-component mixture with an application to plasma
摘要：
考虑了非反应性多组分气体混合物，提出了一类易于推广到多组分的模型。两种物质的混合物是由一个系统的动力学BGK方程，具有两个相互作用的条款，以占的动量和能量之间的物种转移。我们证明了我们的模型的一致性：守恒性质，积极的解决方案的空间均匀的情况下，积极的所有温度，H-定理和收敛到一个全球平衡的空间均匀的情况下，在全球麦克斯韦分布的形式。这样，我们就能导出通常的宏观守恒律。特别地，通过考虑由离子和电子组成的混合物，我们从我们的模型导出了理想MHD的宏观方程。
英文摘要：
We consider a non reactive multi component gas mixture.We propose a class of models, which can be easily generalized to multiple species. The two species mixture is modelled by a system of kinetic BGK equations featuring two interaction terms to account for momentum and energy transfer between the species. We prove consistency of our model: conservation properties, positivity of the solutions for the space homogeneous case, positivity of all temperatures, H-theorem and convergence to a global equilibrium in the space homogeneous case in the form of a global Maxwell distribution. Thus, we are able to derive the usual macroscopic conservation laws. In particular, by considering a mixture composed of ions and electrons, we derive the macroscopic equations of ideal MHD from our model.
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