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

We consider the equations which describe a stationary motion of a viscous compressible barotropic fluid in a bounded domain in ℝ3 with a free boundary determined by the surface tension. By means of some a priori estimates we prove the existence of rotationally symmetric solutions (in reality with some additional symmetry) for a sufficiently small external force and in the case of rotationally symmetric force and domain (where also we need more symmetry, respectively).

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