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Gleichgewichtsfiguren zäher Flüssigkeiten mit Oberflächenspannung (Equilibrium figures of viscous fluids with surface tension). (German) Zbl 0561.76042
We prove the unique solvability of a free boundary value problem for the stationary Navier-Stokes equations: the shape of the free boundary is governed by surface tension. This capillary surface either separates two fluids of different viscosity or bounds a drop of fluid in vacuum. In the latter case the problem can be regarded as a generalization of the classical equilibrium figures.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations
76U05 General theory of rotating fluids
53A10 Minimal surfaces in differential geometry, surfaces with prescribed mean curvature
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