This paper shows the unique solvability of elliptic problems associated with two-phase incompressible flows, which are governed by the two-phase Navier-Stokes equations with a sharp moving interface, in unbounded domains such as the whole space separated by a compact interface and the whole space separated by a non-compact interface. As a by-product, we obtain the Helmholtz-Weyl decomposition for two-phase incompressible flows.

中文翻译：

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与无界域中两相不可压缩流动相关的椭圆问题的独特可解性

本文展示了与两相不可压缩流动相关的椭圆问题的独特可解性，这些问题由具有尖锐移动界面的两相 Navier-Stokes 方程控制，在无界域中，例如由紧凑界面分隔的整个空间和整个空间由一个非紧凑的界面分隔。作为副产品，我们获得了两相不可压缩流的 Helmholtz-Weyl 分解。