Unique solvability of elliptic problems associated with two-phase incompressible flows in unbounded domains

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