On the Comparison Between Phenomenological and Kinetic Theories of Gas Mixtures with Applications to Flocking

We study the compression between the phenomenological and kinetic models fora mixture of gases from the viewpoint of collective dynamics. In the case inwhich constituents are Eulerian gases, balance equations for mass, momentum,and energy are the same in the main differential part, but production terms dueto the interchanges between constituents are different. They coincide only whenthe thermal and mechanical diffusion are sufficiently small. In this paper, wefirst verify that both models satisfy the universal requirements ofconservation laws of total mass, momentum, and energy, Galilean invariance andentropy principle. Following the work of Ha and Ruggeri (ARMA 2017), weconsider spatially homogeneous models which correspond to the generalizationsof the Cucker Smale model with the thermal effect. In these circumstances, weprovide analytical results for the comparison between two resulting models andalso present several numerical simulations to complement analytical results.