Why condensation by compression in pure water vapor cannot occur in an approach based on Euler equations

Phase transitions are in the focus of the modeling of multiphase flows. A large number of models is available to describe such processes. We consider several different two phase models that are based on the Euler equations of compressible fluid flows and which take into account phase transitions between a liquid phase and its vapor. Especially we consider the flow of liquid water and water vapor. We give a mathematical proof, that all these models are not able to describe the process of condensation by compression. This behavior is in agreement with observations in experiments, that simulate adiabatic flows, and shows that the Euler equations give a fairly good description of the process. The mathematical proof is valid for the official standard {\em IAPWS-IF97} for water and for any other good equation of state. Also the opposite case of expanding the liquid phase will be discussed.