Geodesic
Instability of rotating fluid
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Tome 370 (2009), pp. 160-183 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with the problem of stability of uniformly rotating viscous incompressible self-gravitating liquid bounded by a rotationally symmetric free surface. It is proved that it is unstable, if the second variation of the energy functional is not positive. Bibl. – 11 titles. 
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     author = {V. A. Solonnikov},
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V. A. Solonnikov. Instability of rotating fluid. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 40, Tome 370 (2009), pp. 160-183. http://geodesic.mathdoc.fr/item/ZNSL_2009_370_a9/

[1] V. A. Solonnikov, “On the stability of uniformly rotating viscous incompressible self-gravitating liquid”, J. Math. Sci., 152:5 (2008), 4343–4370 | MR

[2] V. A. Solonnikov, “On instability of equilibrium figures of rotating viscous incompressible self-gravitating liquid not subjected to capillary forces”, J. Math. Sci., 139:1 (2006), 6338–6350 | DOI | MR | Zbl

[3] V. A. Solonnikov, “On instability of equilibrium figures of rotating viscous incompressible self-gravitating liquid”, J. Math. Sci., 128 (2005), 3241–3262 | DOI | MR | Zbl

[4] V. A. Solonnikov, “On problem of stability of equilibrium figures of uniformly rotating viscous incompressible liquid”, Instability in models connected with fluid flows, II, Int. Math. Ser., 7, eds. C. Bardos, A. V. Fursikov, Springer, 2007, 189–254 | DOI | MR

[5] V. A. Solonnikov, “On the linear problem related to the stability of uniformly rotating self-gravitating liquid”, J. Math. Sci., 144:6 (2007), 4671–4695 | DOI | MR | Zbl

[6] V. A. Solonnikov, “On the non-stationary motion of a viscous incompressible liquid over a rotating ball”, J. Math. Sci., 157:6 (2009), 885–947 | DOI | MR | Zbl

[7] V. A. Solonnikov, “On a linear problem connected witrh equilibrium figures of a uniformly rotating viscous liquid”, J. Math. Sci., 132:4 (2006), 502–521 | DOI | MR

[8] M. Padula, V. A. Solonnikov, “A simple proof of the linear instability of rotating liquid drops”, Ann. Univ. Ferrara, 54:1 (2008), 107–122 | DOI | MR | Zbl

[9] V. A. Solonnikov, “Estimate of the generalized energy in a free-boundary problem for a viscous incompressible fluid”, J. Math. Sci., 120:5 (2004), 1766–1783 | DOI | MR

[10] O. A. Ladyzhenskaya, V. A. Solonnikov, “The linearization principle and invariant manifolds for problems of magnetohydrodynamics”, J. Sov. Math., 8:4 (1977), 384–422 | DOI | Zbl

[11] V. A. Solonnikov, “On estimates for potentials related to the problem of stability of rotating self-gravitating liquid”, J. Math. Sci., 154:1 (2008), 90–124 | DOI | MR | Zbl