This paper is concerned with a coupled Navier–Stokes/Cahn–Hilliard system describing a diffuse interface model for the two-phase flow of compressible viscous fluids in a bounded domain in one dimension. We prove the existence and uniqueness of global classical solutions for $\rho_0 \in C^{3,\alpha} (I)$. Moreover, we also obtain the global existence of weak solutions and unique strong solutions for $\rho_0 \in H^1 (I)$ and $\rho_0 \in H^2 (I)$, respectively. In these cases, the initial density function $\rho_0$ has a positive lower bound.

中文翻译：

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一维可压缩粘性流体两相流扩散接口模型的整体解

本文涉及一个耦合的Navier-Stokes / Cahn-Hilliard系统，该系统描述了一维有界域中可压缩粘性流体的两相流的扩散界面模型。我们证明了C ^ {3，\ alpha}（I）$中$ \ rho_0 \的全局经典解的存在性和唯一性。此外，我们还分别获得了H ^ 1（I）$中的\ rho_0 \和H ^ 2（I）$中的$ rho_0的弱解和唯一强解的全局存在。在这些情况下，初始密度函数$ \ rho_0 $具有正下限。