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Zapiski Nauchnykh Seminarov POMI, 2007, Volume 348, Pages 165–208 (Mi znsl66)  
This article is cited in 12 scientific papers (total in 12 papers)

On the stability of uniformly rotating viscous incompressible self-gravitating liquid

V. A. Solonnikov

St. Petersburg Department of V. A. Steklov Institute of Mathematics, Russian Academy of Sciences
Full-text PDF (365 kB) Citations (12)
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Abstract: The paper is devoted to justification of the principle of minimum of potential energy in the problem of stability of uniformly rotating viscous incompressible self-gravitating liquid. The capillary forces on the free boundary of the liquid are not taken into account. It is proved that the regime of rigid rotation is stable, if the second variation of the energy functional is positive. The proof is based on the analysis of the evolution free boundary problem for the perturbations of the velocity and the pressure of rotating liquid.
Received: 05.10.2007
English version:
Journal of Mathematical Sciences (New York), 2008, Volume 152, Issue 5, Pages 713–740
DOI: https://doi.org/10.1007/s10958-008-9090-7
Bibliographic databases:
Language: English
Citation: V. A. Solonnikov, “On the stability of uniformly rotating viscous incompressible self-gravitating liquid”, Boundary-value problems of mathematical physics and related problems of function theory. Part 38, Zap. Nauchn. Sem. POMI, 348, POMI, St. Petersburg, 2007, 165–208; J. Math. Sci. (N. Y.), 152:5 (2008), 713–740
Citation in format AMSBIB
\Bibitem{Sol07}
\by V.~A.~Solonnikov
\paper On the stability of uniformly rotating viscous
incompressible self-gravitating liquid
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~38
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 348
\pages 165--208
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl66}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2008
\vol 152
\issue 5
\pages 713--740
\crossref{https://doi.org/10.1007/s10958-008-9090-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-51749116919}
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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