Lecture note 36/2007
Diffuse Interface Models for Two-Phase Flows of Viscous Incompressible Fluids
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Submission date: 26. Oct. 2007 (revised version: February 2008)
Abels, H.: Diffuse interface models for two-phase flows of viscous incompressible fluids
Habilitation, Universität Leipzig, 2008
MSC-Numbers: 76T99, 76D27, 76D03, 76D45, 35B40
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This is my habilitation thesis, which was submitted on October 1st at the University of Leipzig, Faculty of Mathematics and Computer Science. The thesis is concerned with the mathematical analysis of different "diffuse interface models" for two-phase flows of two macroscopically immiscible incompressible, viscous fluids e.g. oil and water. In diffuse interface models the classical sharp interface is replaced by an interfacial region, where a partial mixing of the fluids on a small length scale occurs. The models under consideration are explained and derived briefly. The main part of the thesis contains existence, regularity, and uniqueness results as well as a result on the asymptotic behaviour of a certain class of diffuse interface models with different choices of free energies. In particular, existence of weak solutions for a model for fluids with general (non-matched) density is proved. For a more detailed describtion see the introduction of the thesis.