  The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahn
system with degenerate heat-conductivity
$\kappa(\theta)=\tilde{\kappa}\theta^\beta$ in 1-d is discussed in this paper.
This system is widely used to describe the motion of immiscible two-phase flow
in numerical simulation. The wellposedness for strong solution of this problem
is established with the $H^1$ initial data for density, temperature, velocity,
and the $H^2$ initial data for phase field. The result shows that no
discontinuity of the phase field, vacuum, shock wave, mass or heat
concentration will be developed at any finite time in the whole space. From the
hydrodynamic point of view, this means that no matter how complex the
interaction between the hydrodynamic and phase-field effects, phase separation
will not occur, but the phase transition is possible.
