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On a free boundary problem for viscous incompressible flows. (English) Zbl 1132.76303

Summary: 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 tangential direction to the interface.

MSC:

76D27 Other free boundary flows; Hele-Shaw flows
35Q35 PDEs in connection with fluid mechanics
35R35 Free boundary problems for PDEs
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