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 to mean field (Vlasov type) kinetic equations, as the asymptotic limit of suitable models on a smaller scale. This kind of PDE systems can be considered as simply modelling multicomponent flows in mixtures containing a dispersed phase, such as sprays or aerosols. In this talk we shall give an overview of results of various type obtained in cooperation with E. Bernard, L. Desvillettes, F. Golse.