JournalsifbVol. 9, No. 4pp. 549–589

On a free boundary problem of viscous incompressible flows

  • Yasunori Maekawa

    Hokkaido University, Sapporo, Japan
On a free boundary problem of viscous incompressible flows cover
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Abstract

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.

Cite this article

Yasunori Maekawa, On a free boundary problem of viscous incompressible flows. Interfaces Free Bound. 9 (2007), no. 4, pp. 549–589

DOI 10.4171/IFB/176