# Well-Posedness of a Navier-Stokes/Mean Curvature Flow system

## TL;DR

This paper proves the well-posedness of a coupled Navier-Stokes and mean curvature flow system modeling two-phase incompressible fluids with a sharp interface, establishing existence of strong solutions under certain conditions.

## Contribution

It demonstrates the existence of strong solutions for a coupled Navier-Stokes and mean curvature flow system, linking sharp interface models to diffuse interface limits.

## Key findings

- Existence of strong solutions for small times
- Coupling of Navier-Stokes with mean curvature flow
- Connection to diffuse interface models

## 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.