Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory

Abstract

Discrete velocity models of the Boltzmann equation are of considerable conceptual interest in the kinetic theory of gases, and, at the same time, a fascinating mathematical subject. The last decade has seen a lot of work on this subject, which is reviewed here. We put an emphasis on mathematical aspects, in particular the global existence question, qualitative properties of solutions, explicit solutions, and the fluid dynamical limit. The mechanical background is discussed more concisely in Part I. Numerous contributions concerning other questions are outlined. We try to give a complete reference list up to and including 1985.