论文标题
从Boltzmann方程式对广义雷诺方程的严格推导
Rigorous derivation of the generalized Reynolds equation from the Boltzmann equation
论文作者
论文摘要
我们研究稀薄平板中的固定玻尔兹曼方程，用于稀有气体，分子平均自由路径与膜厚度相当。我们证明存在一种解决方案，该解决方案将流体动力学极限收敛到密度麦克斯韦ian的密度 - 该密度是作为通用雷诺方程的解决方案而获得的。通过仔细估计其余部分，使用截短的希尔伯特扩张证明了收敛性。
We study the stationary Boltzmann equation in a thin slab for a rarefied gas for which the molecular mean free path is comparable to the film thickness. We prove that there exists a solution which converges, in the hydrodynamic limit, to a density Maxwellian -- this density is obtained as the solution to the generalized Reynolds equation. The convergence is proved using a truncated Hilbert expansion by carefully estimating the remainder.
