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On the stability of axially symmetric equilibrium figures of a rotating viscous incompressible fluid
Author(s):
V.
A.
Solonnikov
Translated by:
I. V. Denisova
Original publication:
Algebra i Analiz,
tom 16
(2004),
vypusk 2.
Journal:
St. Petersburg Math. J.
16
(2005),
377-400.
MSC (2000):
Primary 35Q30
Posted:
March 9, 2005
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Abstract:
It is proved that if the second variation of the energy functional  (see (2.9)) is positive, then the axially symmetric equilibrium figure of a viscous incompressible capillary fluid is stable. The proof is based on the study of a nonstationary free boundary problem for the Navier-Stokes system with initial data close to the rotation regime of the fluid as a rigid body.
References:
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- 2.
- P. Appell, Traité de mécanique rationnelle. T. 4, Fasc. I. Figures d'équilibre d'une masse liquide homogène en rotation, Gauthier-Villars, Paris, 1932.
- 3.
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- M. Padula and 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 (Rolduc/Gaeta, 2001), World Sci. Publishing, River Edge, NJ, 2002, pp. 180-203. MR 1937540 (2003h:35210)
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- V. A. Solonnikov, A generalized energy estimate in a problem with a free boundary for a viscous incompressible fluid, Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 282 (2001), 216-243. (Russian) MR 1874890 (2003b:35217)
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Additional Information:
V.
A.
Solonnikov
Affiliation:
St. Petersburg Branch, Steklov Mathematical Institute, Russian Academy of Sciences, Fontanka 27, St. Petersburg 191023, Russia
Email:
solonnik@pdmi.ras.ru
DOI:
10.1090/S1061-0022-05-00855-1
PII:
S 1061-0022(05)00855-1
Keywords:
Equilibrium figures,
free boundary problems,
stability
Received by editor(s):
18/AUG/2003
Posted:
March 9, 2005
Additional Notes:
Supported by RFBR (grant no. 03-01-00638).
Copyright of article:
Copyright
2005,
American Mathematical Society
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