Analysis of a mathematical model of stratified two-phase fluid flow including surface tension effects

We consider a mathematical model of a stratified two-phase fluid flow in one space dimension. Our model consists of a system of PDEs of convection-dispersion type. When the dispertion terms are omitted we prove that the first order system extracted from our model in nowhere hyperbolic in the set of the physically admissible states. We prove hovever the short time existence of smooth solutions of the full model.