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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

 

On the stability of axially symmetric equilibrium figures of a rotating viscous incompressible fluid


Author: V. A. Solonnikov
Translated by: I. V. Denisova
Original publication: Algebra i Analiz, tom 16 (2004), nomer 2.
Journal: St. Petersburg Math. J. 16 (2005), 377-400
MSC (2000): Primary 35Q30
Published electronically: March 9, 2005
MathSciNet review: 2068344
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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that if the second variation of the energy functional $R$ (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.


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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: http://dx.doi.org/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): August 18, 2003
Published electronically: March 9, 2005
Additional Notes: Supported by RFBR (grant no. 03-01-00638).
Article copyright: © Copyright 2005 American Mathematical Society