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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

URN to cite this document:
urn:nbn:de:bvb:355-epub-417046
DOI to cite this document:
10.5283/epub.41704
Terasawa, Y. ; Abels, Helmut
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Date of publication of this fulltext: 27 Feb 2020 15:16


Abstract

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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