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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
117/2006

On the Notion of Generalized Solutions of Viscous Incompressible Two-Phase Flows

Helmut Abels

Abstract

In this article we review different approaches to the existence of solutions of a two-phase flow of two viscous, incompressible fluids globally in time. We compare the known results in the cases with and without surface tension. In particular, we discuss properties of the free surface/ the interface between the two fluids.

Received:
Oct 19, 2006
Published:
Oct 19, 2006
MSC Codes:
35Q30, 35Q35, 76D27, 76D45, 76T99
Keywords:
two-phase flow, free boundary value problems, varifold solutions, measure-valued solutions, surface tension

Related publications

inJournal
2007 Repository Open Access
Helmut Abels

On the notion of generalized solutions of viscous incompressible two-phase flows

In: RIMS Kokyuroku, B1 (2007), pp. 1-19