Existence of weak solutions to steady Navier-Stokes/Allen-Cahn system

作者：Chen, Senming; Ji, Shanming; Wen, Huanyao; Zhu, Changjiang^*

来源：Journal of Differential Equations, 2020, 269(10): 8331-8349.

DOI：10.1016/j.jde.2020.06.026

• Navier-Stokes
• Allen-Cahn
• Weak solution
• Nontrivial solution

The boundary value problem for the three-dimensional steady viscous compressible Navier-Stokes/Allen-Cahn (NSAC) system is considered. We establish the existence of a weak solution for the adiabatic index gamma > 2 with the phase function belonging to [-1, 1 ] . Moreover, we give further analysis on the weak solu-tion. More specifically, we prove that the steady NSAC system degenerates into Navier-Stokes system if the phase function is positive (negative) on (Omega) over bar.