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

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, 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 of the unique solvability of elliptic problems, we obtain the Helmholtz-Weyl decomposition for two-phase incompressible flows.

46 pages

References in corpus (2)

• On the $\mathcal{R}$-boundedness of solution operator families for two-phase Stokes resolvent equations
• Existence of $\mathcal{R}$-bounded solution operator families for a compressible fluid model of Korteweg type on the half-space