Stability of the Rarefaction Wave for a Non-isentropic Navier-Stokes/Allen-Cahn System

This paper is concerned with the large time behavior of solutions to the Cauchy problem for a one-dimensional compressible non-isentropic Navier-Stokes/Allen-Cahn system which is a combination of the classical Navier-Stokes system with an Allen-Cahn phase field description. Motivated by the relationship between Navier-Stokes/Allen-Cahn and Navier-Stokes, the author can prove that the solutions to the one dimensional compressible non-isentropic Navier-Stokes/Allen-Cahn system tend time-asymptotically to the rarefaction wave, where the strength of the rarefaction wave is not required to be small. The proof is mainly based on a basic energy method.