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

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Abstract

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.

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Authors and Affiliations

  1. Universität Regensburg, 93040, Regensburg, Germany

    Helmut Abels, Daniel Depner & Harald Garcke

Authors
  1. Helmut Abels
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  2. Daniel Depner
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  3. Harald Garcke
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Correspondence to Helmut Abels.

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Communicated by Y. Giga

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Abels, H., Depner, D. & Garcke, H. Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities. J. Math. Fluid Mech. 15, 453–480 (2013). https://doi.org/10.1007/s00021-012-0118-x

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