  We introduce a new sharp interface model for the flow of two immiscible,
viscous, incompressible fluids. In contrast to classical models for two-phase
flows we prescribe an evolution law for the interfaces that takes diffusional
effects into account. This leads to a coupled system of Navier-Stokes and
Mullins-Sekerka type parts that coincides with the asymptotic limit of a
diffuse interface model. We prove the long-time existence of weak solutions,
which is an open problem for the classical two-phase model. We show that the
phase interfaces have in almost all points a generalized mean curvature.
