On the symmetry of the linearized Boltzmann equation

Abstract

Relations between different problems described by the linearized Boltzmann equation (LBE) are discussed on the basis of the classical symmetry of LBE and kinetic boundary condition. The theory is developed for the system of arbitrary Knudsen number (Kn) from the view point of the Green function. After showing the main idea of the approach to steady problems for bounded and unbounded domains, its extension to unsteady problems in a fixed bounded domain is given. In particular, in the latter, recovery of Kubo formula for the viscosity and thermal conductivity in the fluctuation–dissipation theorem and its extension to the systems of arbitrary Kn are shown. A comment on the extension to gas mixtures is also given.