In this paper, we study the large-time behavior of solutions to the Navier–Stokes/Allen–Cahn system of compressible viscous gases in half space. We prove that the corresponding stationary solutions of the small amplitude to the inflow problem for the Navier–Stokes/Allen–Cahn system are time-asymptotically stable. The proof of asymptotic stability is based on the basic energy method.

中文翻译：

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耦合可压缩 Navier-Stokes/Allen-Cahn 系统流入问题的稳态稳定性

在本文中，我们研究了半空间中可压缩粘性气体 Navier-Stokes/Allen-Cahn 系统解的大时间行为。我们证明了 Navier-Stokes/Allen-Cahn 系统的流入问题的小振幅对应的平稳解是时间渐近稳定的。渐近稳定性的证明是基于基本能量法。