Free boundary problem for the Navier–Stokes equations for a compressible fluid with a surface tension

The paper is conserned with evolutional problem governing the motion of an isolated mass a viscous compressible liquid whose particles attract each other according to the Newton's law. The liquid is placed in the field of external forces and it is subjected to external pressure and capillary forces at the boundary.
It is proved that this problem has a unique solution belonging to some Sobolev space, on a finite time interval whose magnitude depends on the data of the problem.