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

This article is cited in 3 scientific papers (total in 3 papers)

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  crossref  mathscinet  zmath  isi
    2. V. A. Solonnikov, “Stability of axis-symmetric equilibrium figures of viscous incompressible liquid”, St. Petersburg Math. J., 16:2 (2005), 377–400  mathnet  crossref  mathscinet  zmath
    3. J. Math. Sci. (N. Y.), 136:2 (2006), 3812–3825  mathnet  crossref  mathscinet  zmath
  • Современная математика. Фундаментальные направления
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