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On the notion of generalized solutions of viscous incompressible two-phase flows. (English) Zbl 1119.35042
Summary: 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.

MSC:
35Q30 Navier-Stokes equations
76T99 Multiphase and multicomponent flows
76D27 Other free boundary flows; Hele-Shaw flows
76D45 Capillarity (surface tension) for incompressible viscous fluids
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