Geodesic
On instability of axially symmetric equilibrium figures of rotating viscous incompressible liquid
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 277-297 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that axially symmetric equilibrium figures of uniformly rotating viscous incompressible liquid are unstable when the second variation of the energy functional can take negative values. 
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V. A. Solonnikov. On instability of axially symmetric equilibrium figures of rotating viscous incompressible liquid. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 36, Tome 318 (2004), pp. 277-297. http://geodesic.mathdoc.fr/item/ZNSL_2004_318_a13/

[1] V. A. Solonnikov, “On non-stationary motion of a finite isolated mass of self-gravitating fluid”, Algebra Anal., 1 (1989), 207–249 | MR | Zbl

[2] M. Padula, V. A. Solonnikov, “Existence of non-steady flows of an incompressible viscous drop of fluid in a frame rotating with finite angular velocity”, Elliptic and parabolic problems, World Science Publishing, River Edge, NY, 2002, 180–203 | MR | Zbl

[3] V. A. Solonnikov, “Estimate of a generalized energy in the free boundary problem for viscous incompressible fluid”, Zap. Nauchn. Semin. POMI, 282, 2001, 216–243 | MR | Zbl

[4] V. A. Solonnikov, “On the problem of evolution of an isolated liquid mass”, Sovr. Math. Fund. Napravl., 3 (2003), 43–62 | MR

[5] V. A. Solonnikov, “On the stability of axially symmetric equilibrium figures of rotating viscous incompressible liquid”, Algebra Anal., 16:2 (2004), 120–153 | MR | Zbl

[6] V. A. Solonnikov, “On the stability of non-symmetric equilibrium figures of rotating viscous incompressible liquid”, Interfaces Free Bound., 6:4 (2004) | MR | Zbl

[7] A. M. Lyapunov, Sobranie tsochinenii, T. 3, Izdat. Akad. Nauk SSSR, M., 1959

[8] P. Appell, Figures d'equilibre d'une mass liquide homogéne en rotation, Paris, 1932 | Zbl

[9] V. A. Solonnikov, “On the justification of the quasistationary approximation in the problem of motion of a viscous capillary drop”, Interfaces Free Bound., 1 (1999), 125–173 | DOI | MR | Zbl

[10] V. A. Solonnikov, “Lectures on evolution free boundary problems: classical solutions”, Mathematical aspects of evolving interfaces, Lecture Notes in Math., 182, eds. J. F. Rodrigues, P. L. Colli, Springer, 2003, 123–175 | MR

[11] V. A. Solonnikov, “Estimates for the resolvent of the operator appearing in the study of equilibrium figures of a rotating viscous incompressible liquid”, Problems Math. Anal., 29 (2004), 105–118 | MR | Zbl

[12] V. A. Solonnikov, “On linear stability and instability of equilibrium figures of uniformly rotating liquid”, Proc. Conf. on Elliptic and Parab. Problems, Taiwan, 2004 (to appear) | MR

[13] T. Nishida, Y. Teramoto, H. Yoshihara, “Global in time behavior of viscous surface waves: horizontally periodic motion”, J. Math. Kyoto Univ. (to appear) | MR

[14] O. A. Ladyzhenskaya, V. A. Solonnikov, “The linearization principle and invariant manifolds in problems of magnetohydrodynamics”, Zap. Nauchn. Semin., LOMI, 38, 1973, 46–93 | MR | Zbl