JournalsifbVol. 15, No. 1pp. 39–75

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

  • Helmut Abels

    Universität Regensburg, Germany
  • Mathias Wilke

    Martin-Luther-Universität Halle-Wittenberg, Germany
Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system cover
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Abstract

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.

Cite this article

Helmut Abels, Mathias Wilke, Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system. Interfaces Free Bound. 15 (2013), no. 1, pp. 39–75

DOI 10.4171/IFB/294