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

2017/05/30 by Helmut Abels, Abels, Helmut, Maximilian Moser +1
Mathematics · #35Q30 #35R35 #76D27 #76D45 #76T99 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q30 #msc:35R35 #msc:76D27 #msc:76D45 #msc:76T99

paper · pdf · doi:10.48550/arxiv.1705.10832

32 pages

arxiv created 2017/05/30 · arxiv updated 2017/06/01

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.

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