Abstract
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.
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