On the well-posedness of the Boltzmann's moment system of equations in fourth approximation

Abstract

We study the one-dimensional non-linear non-stationary Boltzmann's moment system of equations in fourth approxi- mation with the tools developed by Sakabekov in [4],[5] and [6]. For the third approximation system Sakabekov proves the mass conservation law (cf. Theorem 2.1 in [4]) and discusses the existence and uniqueness of the solution (cf. Theorem in [6]). We extend the analysis of the existence and uniqueness of the solution to the fourth approximation system. In particular, for the fourth approximation system we discuss the well-posed initial and boundary value problem and obtain the a-priori estimate of the solution belonging to the space of functions, continuous in time and square summable by spatial variable.