Maekawa, Yasunori On a free boundary problem for viscous incompressible flows. (English) Zbl 1132.76303 Interfaces Free Bound. 9, No. 4, 549-589 (2007). 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. Cited in 2 Documents MSC: 76D27 Other free boundary flows; Hele-Shaw flows 35Q35 PDEs in connection with fluid mechanics 35R35 Free boundary problems for PDEs PDFBibTeX XMLCite \textit{Y. Maekawa}, Interfaces Free Bound. 9, No. 4, 549--589 (2007; Zbl 1132.76303) Full Text: DOI