Geodesic
Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system
Helmut Abels1 ; Mathias Wilke2
1Universität Regensburg, Germany
2Martin-Luther-Universität Halle-Wittenberg, Germany
Interfaces and free boundaries, Tome 15 (2013) no. 1, pp. 39-75

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DOI

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.
DOI : 10.4171/ifb/294
Classification : 35-XX, 76-XX, 00-XX
Mots-clés : Two-phase flow, Navier–Stokes system, Free boundary problems, Mullins–Sekerka equation, convergence to equilibria

Helmut Abels  1   ; Mathias Wilke  2

1 Universität Regensburg, Germany
2 Martin-Luther-Universität Halle-Wittenberg, Germany 
Helmut Abels; Mathias Wilke. Well-posedness and qualitative behaviour of solutions for a two-phase Navier–Stokes-Mullins–Sekerka system. Interfaces and free boundaries, Tome 15 (2013) no. 1, pp. 39-75. doi: 10.4171/ifb/294
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