On stability of solutions to the two-fuid models for dispersed two-phase flow

Abstract: In this thesis the two-fluid (Eulerian/Eulerian) formulationfor dispersed two-phase flow is considered. The inviscidformulation in one space dimension is known to be conditionallywell-posed. On the other hand the viscous formulation islocally in time well-posed for smooth initial data, but with amedium to high wave number instability. In this study weconsider two issues.First, we study the long time behavior of the viscous modelin one space dimension, where we rely on numerical experiments.We try to regularize the problem in a standard way. Thesimulations suggest that it is not possible to regularize in astandard way.Secondly, we analyze the inviscid formulation in two spacedimensions. Similar condition for well-posedness is obtained asfor the inviscid formulation in one space dimension.