Kinetic Theory of Gas

The motivations that suggested the publication of this book in 1969 are still largely valid. In this revised edition I have updated the literature on the subjects that were covered in the original version; I have also added an appendix to Chapter VI, explaining the technique for solving singular integral equations and systems of such equations. In addition I have tried to give an introduction to the important developments concerning the purely mathematical theory (existence and uniqueness theorems). This part of kinetic theory has reached a mature stage in the last few years and is relevant for both the physical foundations of the subject (validity of the Boltzmann equation) and the application of kinetic theory to rarefied gas dynamics (numerical and simulation methods).

The kinetic theory of gases as we know it dates to the paper of Boltzmann in 1872. The justification and context of this equation has been clarified over the past half century to the extent that it comprises one of the most complete examples of many-body analyses exhibiting the contraction from a microscopic to a mesoscopic description.

This monograph is intended to provide a comprehensive description of the rela­ tion between kinetic theory and fluid dynamics for a time-independent behavior of a gas in a general domain. A gas in a steady (or time-independent) state in a general domain is considered, and its asymptotic behavior for small Knudsen numbers is studied on the basis of kinetic theory. Fluid-dynamic-type equations and their associated boundary conditions, together with their Knudsen-layer corrections, describing the asymptotic behavior of the gas for small Knudsen numbers are presented.