Title: Well-Posedness of a Navier-Stokes/Mean Curvature Flow system,
Abstract: We consider a two-phase flow of two incompressible, viscous and immiscible
fluids which are separated by a sharp interface in the case of a simple phase
transition. In this model the interface is no longer material and its evolution
is governed by a convective mean curvature flow equation, which is coupled to a
two-phase Navier-Stokes equation with Young-Laplace law. The problem arises as
a sharp interface limit of a diffuse interface model, which consists of a
Navier-Stokes system coupled with an Allen-Cahn equation. We prove existence of
strong solutions for sufficiently small times and regular initial data.