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.

Fluid flow simulations that involve deforming domains, in the presence of one or more moving boundaries or fluidfluid interfaces, continue to present unique challenges, and form one of the frontiers of computational science. Freesurface flows in particular involve the motion of the fluid interface which is unknown at the outset of the simulation. Thus, both the domain and the flow field are par...