On the Notion of Generalized Solutions of Viscous Incompressible Two-Phase Flows
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Submission date: 19. Oct. 2006
published in: RIMS Kokyuroku, B1 (2007), p. 1-19
MSC-Numbers: 35Q30, 35Q35, 76D27, 76D45, 76T99
Keywords and phrases: two-phase flow, free boundary value problems, varifold solutions, measure-valued solutions, surface tension
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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.