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

Solonnikov, V.

doi:10.1090/S1061-0022-05-00855-1

On the stability of axially symmetric equilibrium figures of a rotating viscous incompressible fluid
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by V. A. Solonnikov
Translated by: I. V. Denisova

St. Petersburg Math. J. 16 (2005), 377-400

DOI: https://doi.org/10.1090/S1061-0022-05-00855-1

Published electronically: March 9, 2005

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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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