Approximate solutions of the Boltzmann equation with infinitely many modes

Abstract

For the nonlinear kinetic Boltzmann equation in the case of a model of hard spheres, we construct an approximate solution in the form of a series of Maxwellian distributions with coefficient functions of time and the space coordinate. We establish the sufficient conditions for the coefficient functions and the values of hydrodynamic parameters appearing in the distribution that enable us to make the analyzed deviation arbitrarily small.