Theory of the Boltzmann Equation (Classic Reprint)

Abstract We present a survey of recent developments In the theory of theB oltzmann equation for a dilute monatomlc gas. These advances are characterized by Increased sophistication In mathematical techniques, Improved understanding of the significance of older approximate results, and a general trend away from adhoc and toward more precise mathematical procedures. In the singular limit of small, mean free path, the traditional Hllbert and Chapman-E nskog expansions have been shown to be asymptotic to true solutions of theB oltzmann equation, but only when the variables are appropriately interpreted. At the opposite extreme of large mean free path where the behavior Is again nonuniform, the precise mathematical singularities have been exposed. Over the whole range of linear problems the presence of a continuous spectrum In both the collision operator and the streaming operator points to the Inadequacy of traditional exponential normal mode expansions In both Initial and boundary value problems. Results in all the reglm.es have been tied together by the overall qualitative understanding given by a more comprehensive existence theory which, for the first time, is broad enough to encompass the transition to macroscopic continuum flow.
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