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The Cauchy problem for non-isentropic compressible Navier-Stokes/Allen-Cahnsystem 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 flowin numerical simulation. The wellposedness for strong solution of this problemis established with the $H^1$ initial data for density, temperature, velocity,and the $H^2$ initial data for phase field. The result shows that nodiscontinuity of the phase field, vacuum, shock wave, mass or heatconcentration will be developed at any finite time in the whole space. From thehydrodynamic point of view, this means that no matter how complex theinteraction between the hydrodynamic and phase-field effects, phase separationwill not occur, but the phase transition is possible.

The Cauchy Problem for Non-Isentropic compressible Navier-Stokes/Allen-Cahn system with Degenerate Heat-Conductivity