Rarefied gas models with velocity dependent collision frequencies

Abstract

Linearized model Boltzmann equations with realistic velocity dependent collision frequencies are investigated. Results obtained on the resolvent of the full hard-sphere and Maxwell Boltzmann equations establish qualitatives similarity in behavior between the classical Boltzmann equations of rarefied gases and their degenerate kernel approximations. This similarity holds also for the analytic continuation into the continuous spectrum of the Boltzmann operators. Comparison is made with the Grad 1,2 and Sirovich 3,4 theories.