SELF-SIMILAR FLUID-DYNAMIC LIMITS FOR THE BROADWELL SYSTEM

This report discusses a new approach for the resolution of the fluid-d ynamic limit for the Broadwell system of the kinetic theory of gases, appropriate in the case of Riemann, Maxwellian data. Since the formal limiting system is expected to have self-similar solutions, we are mot ivated to replace the Knudsen number epsilon in the Broadwell model so that the resulting model admits self-similar solutions xi = x/t and t hen let epsilon go to zero. The limiting procedure is justified and th e resulting limit is a solution of the Riemann problem for the fluid-d ynamic limit equations. A class of Riemann data for which this program can be carried out is exhibited. Furthermore, it is shown that for th e Carleman model the complete program can be done successfully for arb itrary Riemann data.