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

  • * Corresponding author: Xin Zhang

    * Corresponding author: Xin Zhang

TThe first author was supported by JSPS KAKENHI Grant Number JP17K14224, and the second author was supported by the Top Global University Project

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  • 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.

    Mathematics Subject Classification: Primary: 35Q30; Secondary: 76D07.


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