On a model for mixture flows: derivation, dissipation and stability properties (Q261281)

A new model of fluid-kinetic origin, coupling the heterogeneous Navier-Stokes system with a constraint on the mean volume velocity of the flow, is proposed for mixture flows. This system is derived from a microscopic model involving a Vlasov-type equation describing the disperse phase, through the passage to a hydrodynamic limit. This model features dissipation properties that permitted the authors to obtain stability of weak solutions in the case of one-dimensional space.