Geodesic
On the stability of uniformly rotating viscous
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 165-208

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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. 
@article{ZNSL_2007_348_a6,
     author = {V. A. Solonnikov},
     title = {On the stability of uniformly rotating viscous},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {165--208},
     publisher = {mathdoc},
     volume = {348},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a6/}
}
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V. A. Solonnikov. On the stability of uniformly rotating viscous. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Tome 348 (2007), pp. 165-208. http://geodesic.mathdoc.fr/item/ZNSL_2007_348_a6/