Some mathematical and physical problems in the kinetic theories of dense fluids

I consider various kinetic models of inert/reacting rare/dense mixtures. In contrast to the previously considered reacting models, the microscopic reversibility (detailed balance) is built-in in the models and thus all mathematical aspects of the models can be fully justified. In the presented kinetic models, the molecules behave as if they were single mass points with two internal states. Collisions may alter the internal states of the molecules, and this occurs when the kinetic energy associated with the reactive motion exceeds the activation energy. For the resulting partial-integral differential equations, I provide fundamental physical and mathematical properties concerning the consistency of the models, the entropy inequality, the existence of solutions, the characterization of the equilibrium solutions, and possible existence of phase transitions.