In this talk we consider the so-called Navier-Stokes-Allen-Cahn as
well as Navier-Stokes-Cahn-Hilliard system. These equations are
combinations of the compressible Navier-Stokes equations with a
Allen-Cahn or Cahn-Hilliard phase field description. These models
admit of describing two-phase patterns in a flowing liquid with or
without phase transformations.
The main focus of this talk relies on investigating linear equations
that are obtained by considering the deviation from equilibrium.
The spectrum of the associated linear operators is analysed.
The purpose is then to conclude linear stability/instability by using
the localization of the spectrum.