On a free boundary problem of viscous incompressible flows
Yasunori Maekawa · Interfaces and Free Boundaries Mathematical Analysis Computation and Applications · 2007
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.