Quasistationary hydrodynamics for the Boltzmann equation

Abstract

The Boltzmann equation solutions are considered for small Knudsen number. The main attention is devoted to certain deviations from the classical Navier-Stokes description. The equations for the quasistationary slow flows are derived. These equations do not contain the Knudsen number and provide in this sense a limiting description of hydrodynamic variables. In the isothermal case the equations reduce to incompressible Navier-Stokes equations for bulk velocity and pressure; in the stationary case they coincide with the equations of slow nonisothermal flows. It is shown that the derived equations, unlike the Burnett equations, possess all principal properties of the Boltzmann equation. In one dimension the equations reduce to a nonlinear diffusion equation, being exactly solvable for Maxwell molecules. Multidimensional stationary heat transfer problems are also discussed. It is shown that one can expect an essential difference between the Boltzmann equation solution in the limit of continuous media and the corresponding solution of Navier-Stokes equations.