| Abstract: | The structure of the Chapman-Enskog solution of the Boltzmann equation linearized with respect to the absolute Maxwell equilibrium is studied. Under the assumption of uniqueness and existence of a solution it is shown that in the steady case the series describing the transport phenomena consist of a finite number of terms, and the heat fluxes and diffusion rates are given by the Burnett approximation and the stresses by the super-Burnett approximation, the following terms of the series vanishing. At the same time, the gas-dynamic variables in all approximations in the small Knudsen number K satisfy the conservation equations in the Stokes approximation; the forces and moments acting on bodies placed in a mixture of gases can be calculated from the Navier-Stokes stresses without allowance for their  reprocessing in Knudsen layers. A problem is formulated for a simple gas, and the transport properties are analyzed by using the invariance properties of the linearized Boltzmann equation and by means of the algorithm of the Chapman-Enskog method, and then the results are generalized to a mixture of gases, and the question of the forces and moments is considered.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 157–163, July–August, 1988.I thank M. N. Gaidukov and O. G. Fridlender for fruitful discussions. |
