Non-Hyperbolicity of the Two-Phase Flow Equations and Kelvin-Helmholtz Instability

The main subject of this paper is the so-called the basic two-phase model. Although this model is about 30 years old and gives a possibility to study mixed flow, there are many defects in it. The main defect of the two-phase model is ill-posedness. Usually, the reason of ill-posedness connected with the average processes used in deriving the model. However, all attempts to take some additional details into account have provided desired results for special cases only. The most mysterious property of the governing two-phase system is nonhyperbolicity. Moreover the system becomes nonhyperbolic if |u₁ - u₂| < $\delta$ , where u₁, u₂ are the velocities of the phases. This paper is an attempt to explain some phenomena connected with the basic two-phase model. All the results can be generalized to a multi-phase case by natural way.