On linearization of the Boltzmann equation

Abstract

The velocity distribution function for particles of a spatially inhomogencous gas confined in a vessel is considered as a solution of the nonlinear Boltzmann kinetic equation. Finite collision frequency is assumed. An external potential force acting upon the particles is imposed, an initial condition is given, and the interaction between the particles of the gas and the walls of the vessel is represented by a short-ranging repulsive potential force acting within a neighbourhood of the walls of the vessel. The linearization of the problem is studied, including the cases the solution cannot be approximated by a Maxwellian distribution. A sequence {f ^j} of iterations is constructed such that f ^j+1 is a solution of the problem linearized around f ^j . It is proved that the iterations converge in a convenient Banach function space to the mild solution of the original nonlinear problem provided the initial approximation is chosen close enough to the solution, and an estimate of the convergence rale is found.