This paper proposes two different approaches for deriving the Vlasov-Navier–Stokes (or Vlasov-Stokes) system used in the theory of ‘thin’ aerosol flows from two kinds of microscopic models. One approach is based on homogenization techniques for elliptic equations in domains with holes, whereas the other approach is based on the various mathematical tools used to study the fluid dynamic limits of the Boltzmann equation.

中文翻译：

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从气体动力学理论到气溶胶流动模型

本文提出了两种不同的方法，用于从两种微观模型中推导用于“稀薄”气溶胶流动理论的Vlasov-Navier-Stokes（或Vlasov-Stokes）系统。一种方法基于带孔域椭圆方程的均化技术，而另一种方法则基于用于研究玻尔兹曼方程的流体动力学极限的各种数学工具。