Asymptotic Stability of Phase Separation States for Compressible Immiscible Two-Phase Flow with Periodic Boundary Condition in 3D

This paper is concerned with a diffuse interface model called as Navier-Stokes/Cahn-Hilliard system. This model is usually used to describe the motion of immiscible two-phase flow with diffusion interface. For the periodic boundary value problem of this system in torus $\mathbb{T}^3$, we prove that there exists a global unique strong solution near the phase separation state, which means no vacuum, shock wave, mass concentration, interface collision and rupture will be developed in finite time. Furthermore, we established the large time behavior of these global strong solution of this system. In particular, we find that the phase field decays algebraically to the phase separation state.