ON NONSTATIONARY MOTION OF A COMPRESSIBLE BAROTROPIC VISCOUS CAPILLARY FLUID BOUNDED BY A FREE-SURFACE

The author considers the motion of a viscous compressible barotropic fluid in R(3), bounded by a free surface that is under surface tension and constant exterior pressure. Assuming the initial density is sufficiently close to a constant, the initial domain is sufficiently close to a ball, the initial velocity is sufficiently small, and the external force vanishes, the existence of a global-in-time solution is proven, which satisfies, at any moment of time, the properties prescribed at the initial moment.