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Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities and Nonlocal Free Energies

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Terasawa, Y. ; Abels, Helmut
License: Creative Commons Attribution 4.0
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Date of publication of this fulltext: 27 Feb 2020 15:16

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We consider a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions and prove existence of weak solutions for it. In contrast to earlier contributions, we study a model with a singular nonlocal free energy, which controls the H-alpha/2-norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization.

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