About the validation of models for multicomponent systems

We shall discuss the derivation of systems of partial differ-ential equations, where hydrodynamic equations are coupled tomean field (Vlasov type) kinetic equations, as the asymptoticlimit of suitable models on a smaller scale. This kind of PDEsystems can be considered as simply modelling multicomponentflows in mixtures containing a dispersed phase, such as spraysor aerosols. In this talk we shall give an overview of resultsof various type obtained in cooperation with E. Bernard, L.Desvillettes, F. Golse.