On the stability of a uniformly rotating viscous incompressible self-gravitating liquid

The paper is devoted to justification of the potential energy minimum principle in the problem of stability of a uniformly rotating viscous incompressible self-gravitating liquid. The capillary forces on the free boundary of the liquid are not taken into account. It is proved that the regime of rigid rotation is stable if the second variation of the energy functional is positive. The proof is based on the analysis of the evolution free boundary problem for perturbations in the velocity and pressure of the rotating liquid. Bibliography: 15 titles. Published in Zapiski Nauchnykh Seminarov POMI, Vol. 348, 2007, pp. 165–208.