We shall discuss a free boundary problem for viscous incompressible fluids which is motivated by the phase transition of materials in a flowing fluid. The problem is formulated as the coupled Stokes/mean curvature equations. Our model is also regarded as the relaxation of a two-phase free boundary problem with surface tension on the interface. We shall construct a unique time-local solution of the problem by establishing the optimal regularity of the velocity field in the tangential directions to the interface.
|Number of pages||41|
|Journal||Interfaces and Free Boundaries|
|Publication status||Published - 2007 Dec 1|
ASJC Scopus subject areas
- Surfaces and Interfaces