A mathematical study of the conservation equation for two-phase mixtures

We study the invariance under the Galilean transformations of the Baer - Nunziato equations for interpenetrating interacting flows which describe the transition from combustion to explosion in two-phase mixtures. We show that the original Baer - Nunziato model is invariant. In addition, we establish the invariance of the kinetic and total energy equations for the components and mixture. But the conservation equations for the total energy of the mixture in the Baer - Nunziato model and in the model of Nigmatulin's group have different behavior. Thus, additional study is required to choose the model describing more adequately the transition from combustion to explosion in two-phase mixtures.