Stability of rotating liquid drops with surface tension

The aim of this paper is to investigate the stability of a stationary solution of free boundary problems of the incompressible Navier–Stokes equations in a three-dimensional bounded domain with surface tension. More precisely, this article proves that if the initial angular momentum is sufficiently small and if the initial configuration is sufficiently close to equilibrium, then there exists a global classical solution that converges exponentially fast to a uniform rigid rotation of the liquid as \(t \rightarrow \infty \) $t\to \infty$ with respect to a certain axis. The proof of the unique existence of a stationary solution is also given.