On a free boundary problem for the stationary Navier-Stokes equations

We investigate stationary flows in a fluid body together with its free boundary. The fluid is assumed to be viscous and incompressible; the free boundary is governed by continuity of the normal stress. Hence the configuration to be considered here can be regarded as a generalization of a classical equilibrium figure. The main tool in proving existence of a regular solution consists in a hard implicit function theorem. © 2016 L'Association Publications de l'Institut Henri Poincaré