The goal of this review paper is to provide the reader with a concise introduction to the
mathematical theory of collision processes in (dilute) gases and plasmas, viewed as a …

2 Chapter 1. Introduction on. Owing to the derivation of the Navier~ Stokes set of equations,
Chapman~ Enskog expansion is mainly referred to when the relation between fluid …

We consider solutions of the Boltzmann equation, in ad‐dimensional torus, d= 2, 3, For
macroscopic times τ= t/ϵN, ϵ «1, t≧ 0, when the space variations are on a macroscopic …

Shear flow and thermal creep flow (flow induced by the temperature gradient along the
boundary wall) of a rarefied gas over a plane wall are considered on the basis of the …

We introduce an elementary energy method for the Boltzmann equation based on a
decomposition of the equation into macroscopic and microscopic components. The …

F≡ F (x, y, z, vx, vy, vz)≥ 0 that is the density of particle located at the position (x, y, z) with
the velocity v=(vx, vy, vz)∈ R3. Everywhere in this paper, we assume that the steady state …

A semi‐infinite expanse of a rarefied gas over a plane wall where there is a constant heat
flow normal to the wall from infinity is considered. The behavior of the gas is analyzed …

The contact discontinuity is one of the basic wave patterns in gas motions. The stability of
contact discontinuities with general perturbations for the Navier–Stokes equations and the …

Despite its conceptual and practical importance, a rigorous derivation of the steady
incompressible Navier–Stokes–Fourier system from the Boltzmann theory has been an …

We study the pointwise behavior of the Green function of the Boltzmann equation. Our
results reveal the particle and fluid aspects of the equation. The particle aspect is …