一类Boltzmann型方程的粗定解
Grossly Determined Solutions for a Boltzmann-like Equation
摘要：
在气体动力学中，由纳维-斯托克斯方程提供的连续介质物理模型与由气体动力学理论提供的热方程和分子模型之间的联系已经被理解了一段时间，特别是通过查普曼和恩斯科格的工作，但它从未被严格地建立。本文通过一个简单的线性类玻尔兹曼方程在这两个模型之间建立了一个精确的桥梁。特别是一类特殊的解决方案，粗略确定的解决方案，这个动力学模型的存在，并满足封闭形式的平衡方程，代表一类连续模型的解决方案。
英文摘要：
In gas dynamics, the connection between the continuum physics model offered by the Navier-Stokes equations and the heat equation and the molecular model offered by the kinetic theory of gases has been understood for some time, especially through the work of Chapman and Enskog, but it has never been established rigorously. This paper established a precise bridge between this two models for a simple linear Boltzman-like equation. Specifically a special class of solutions, the grossly determined solutions, of this kinetic model are shown to exist and satisfy closed form balance equations representing a class of continuum model solutions.
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