Journal of Mathematical Fluid Mechanics

, Volume 15, Issue 3, pp 453–480 | Cite as

Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities

  • Helmut AbelsEmail author
  • Daniel Depner
  • Harald Garcke


We prove existence of weak solutions for a diffuse interface model for the flow of two viscous incompressible Newtonian fluids in a bounded domain in two and three space dimensions. In contrast to previous works, we study a new model recently developed by Abels et al. for fluids with different densities, which leads to a solenoidal velocity field. The model is given by a non-homogeneous Navier–Stokes system with a modified convective term coupled to a Cahn–Hilliard system. The density of the mixture depends on an order parameter.

Mathematics Subject Classification (2010)

Primary 76T99 Secondary 35Q30 35Q35 76D03 76D05 76D27 76D45 


Two-phase flow Navier–Stokes equation Diffuse interface model Mixtures of viscous fluids Cahn–Hilliard equation 


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© Springer Basel 2012

Authors and Affiliations

  1. 1.Universität RegensburgRegensburgGermany

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