Interfaces and Free Boundaries


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Volume 15, Issue 1, 2013, pp. 39–75
DOI: 10.4171/IFB/294

Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system

Helmut Abels[1] and Mathias Wilke[2]

(1) Departement Mathematik, Universität Regensburg, Universitätsstraße 31, 93053, REGENSBURG, GERMANY
(2) Institut für Mathematik, Martin-Luther-Universität Halle-Wittenberg, Theodor-Lieser-Straße 5, 06120, HALLE, GERMANY

We consider a two-phase problem for two incompressible, viscous and immiscible fluids which are separated by a sharp interface. The problem arises as a sharp interface limit of a diffuse interface model. We present results on local existence of strong solutions and on the long-time behavior of solutions which start close to an equilibrium. To be precise, we show that as time tends to infinity, the velocity field converges to zero and the interface converges to a sphere at an exponential rate.

Keywords: Two-phase flow, Navier–Stokes system, Free boundary problems, Mullins–Sekerka equation, convergence to equilibria

Abels Helmut, Wilke Mathias: Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system. Interfaces Free Bound. 15 (2013), 39-75. doi: 10.4171/IFB/294