Abstract
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.
Acknowledgements
Ting Luo would like to thank Professors Changjiang Zhu and Haiyan Yin for many fruitful discussions on the topic of the paper. Ting Luo was supported by the National Natural Science Foundation of China 12001249, the Educational Commission Science Programm of Jiangxi Province GJJ190280 and the Scientific Research Funds of Jiangxi University of Finance and Economics 012270624.
Disclosure statement
No potential conflict of interest was reported by the author(s).