Abstract
The author considers the motion of a viscous compressible barotropic fluid in $\mathbb{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.
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