The asymptotic stability of phase separation states for compressible immiscible two-phase flow in 3D. (English) Zbl 1524.76489
Summary: This paper is concerned with a diffuse interface model called Navier-Stokes/Cahn-Hilliard system. This model is usually used to describe the motion of immiscible two-phase flows with a 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 that no vacuum, shock wave, mass concentration, interface collision or rupture will be developed in finite time. Furthermore, we establish the large time behavior of the global strong solution of this system. In particular, we find that the phase field decays algebraically to the phase separation state.
MSC:
| 76T10 | Liquid-gas two-phase flows, bubbly flows |
| 35B40 | Asymptotic behavior of solutions to PDEs |
| 35B65 | Smoothness and regularity of solutions to PDEs |
| 35L65 | Hyperbolic conservation laws |
| 76N06 | Compressible Navier-Stokes equations |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
Keywords:
Navier-Stokes/Cahn-Hilliard system; strong solution; existence; uniqueness; large-time behaviorReferences:
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