This paper is devoted to the study of the nonlinear stability of the composite wave consisting of two rarefaction waves and a viscous contact wave for the Cauchy problem to 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. We first construct the composite wave through Euler equations under the assumption of [Formula: see text] for the large time behavior, and then prove that the composite wave is time asymptotically stable under small perturbations for the corresponding Cauchy problem of the non-isentropic Navier–Stokes/Allen–Cahn system. The proof is mainly based on a basic energy method.

中文翻译：

---

可压缩 Navier-Stokes/Allen-Cahn 系统复合波的稳定性

本文致力于研究由两个稀疏波和一个粘性接触波组成的复合波对一维可压缩非等熵 Navier-Stokes/Allen-Cahn 系统的 Cauchy 问题的非线性稳定性，该系统是一个组合具有 Allen-Cahn 相场描述的经典 Navier-Stokes 系统。我们首先在[公式：见正文]的大时间行为假设下通过欧拉方程构造复合波，然后证明非等熵纳维的相应柯西问题在小扰动下复合波是时间渐近稳定的-斯托克斯/艾伦-卡恩系统。证明主要基于一种基本能量法。