Abstract:
The paper is devoted to justification of the
principle of minimum of potential energy in the problem of
stability of 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 the perturbations of
the velocity and the pressure of rotating liquid.
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