THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D*

doi:10.1007/s10473-023-0513-9

摘要/Abstract

摘要： 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.

关键词: Navier-Stokes/Cahn-Hilliard system, strong solution, existence, uniqueness, large-time behavior

Abstract: 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.

Key words: Navier-Stokes/Cahn-Hilliard system, strong solution, existence, uniqueness, large-time behavior

中图分类号:

35B40

Yazhou CHEN, Hakho HONG, Xiaoding SHI. THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D^*[J]. 数学物理学报(英文版), 2023, 43(5): 2133-2158.

Yazhou CHEN, Hakho HONG, Xiaoding SHI. THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D^*[J]. Acta mathematica scientia,Series B, 2023, 43(5): 2133-2158.

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THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D^*

THE ASYMPTOTIC STABILITY OF PHASE SEPARATION STATES FOR COMPRESSIBLE IMMISCIBLE TWO-PHASE FLOW IN 3D^*

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