Asymptotics of the Boltzmann Equation and Fluid Dynamics

Abstract

The relations and differences between the Boltzmann equation and the fluid dynamic equations is one of the most interesting features of kinetic theory. In these four lectures at CISM in Udine I present an outline of this theory and some of its main results: derivation and validity of the fluid equations using the Hilbert and Chapman-Enskog expansions, description of shock waves, boundary layer solutions, and fluid dynamics of discrete velocity models. The objective of these lectures is to present rigorous results with solid physical meaning and to suggest further lines of research.

The work described here was supported in part by the Air Force Office of Scientific Research through grants AFOSR-85-0017, and AFOSR-86-0352.