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 CMFD, 2003, Volume 3, Pages 43–62 (Mi cmfd15)

On the Problem of Evolution of an Isolated Liquid Mass

V. A. Solonnikov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences

Abstract: The paper is concerned with the problem of stability of equilibrium figures of a uniformly rotating, viscous, incompressible, self-gravitating liquid subjected to capillary forces at the boundary. It is shown that a rotationally symmetric equilibrium figure $F$ is exponentially stable if the functional $G$ defined on the set of domains $\Omega$ close to $F$ and satisfying the conditions of volume invariance ($|\Omega|=|F|$) and the barycenter position attains its minimum for $\Omega=F$. The proof is based on the direct analysis of the corresponding evolution problem with initial data close to the regime of a rigid rotation.

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English version:
Journal of Mathematical Sciences, 2004, 124:6, 5442–5460

Bibliographic databases:

UDC: 517.95+517.958

Citation: V. A. Solonnikov, “On the Problem of Evolution of an Isolated Liquid Mass”, Proceedings of the International Conference on Differential and Functional-Differential Equations — Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11–17 August, 2002). Part 3, CMFD, 3, MAI, M., 2003, 43–62; Journal of Mathematical Sciences, 124:6 (2004), 5442–5460

Citation in format AMSBIB
\Bibitem{Sol03} \by V.~A.~Solonnikov \paper On the Problem of Evolution of an Isolated Liquid Mass \inbook Proceedings of the International Conference on Differential and Functional-Differential Equations --- Satellite of International Congress of Mathematicians ICM-2002 (Moscow, MAI, 11--17 August, 2002). Part~3 \serial CMFD \yr 2003 \vol 3 \pages 43--62 \publ MAI \publaddr M. \mathnet{http://mi.mathnet.ru/cmfd15} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2129144} \zmath{https://zbmath.org/?q=an:1071.76023} \transl \jour Journal of Mathematical Sciences \yr 2004 \vol 124 \issue 6 \pages 5442--5460 \crossref{https://doi.org/10.1023/B:JOTH.0000047363.01729.71} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. V. A. Solonnikov, “On the stability of nonsymmetric equilibrium figures of a rotating viscous incompressible liquid”, Interfaces and Free Boundaries, 6:4 (2004), 461–492
2. V. A. Solonnikov, “Stability of axis-symmetric equilibrium figures of viscous incompressible liquid”, St. Petersburg Math. J., 16:2 (2005), 377–400
3. J. Math. Sci. (N. Y.), 136:2 (2006), 3812–3825
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