Stability of stationary for inflow problem on the coupled compressible Navier-Stokes/Allen-Cahn system. (English) Zbl 1498.35049
Summary: 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.
MSC:
| 35B35 | Stability in context of PDEs |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35Q35 | PDEs in connection with fluid mechanics |
Keywords:
Navier-Stokes/Allen-Cahn system; inflow problem; stability of small amplitude stationary solutions; half space problemReferences:
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