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Mat. Sb., 1994, Volume 185, Number 5, Pages 139–159 (Mi msb900)  

This article is cited in 2 scientific papers (total in 2 papers)

Linear stability of equilibria of a fluid that is a nonconductor of heat

V. I. Yudovich


Abstract: Convective stability is studied in the linear approximation of equilibria of a strongly viscous fluid that is a nonconductor of heat where the fluid fills a bounded domain in a gravitational field. The corresponding system consists of the heat equation with transport in a velocity field and the steady-state Stokes system for the velocity and pressure. The latter includes an Archimedean force proportional to the temperature.
It is proved that equilibria for which the temperature strictly increases upward are stable in $L_2$ with respect to the temperature and in $W_2^2$ with respect to the velocity. Here, however, perturbations may die out arbitrarily slowly (Banach–Steinhaus stability). Under rough violation of the condition of monotonicity of the temperature the equilibrium is unstable.
Some critical cases of stability are also considered.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:1, 117–134

Bibliographic databases:

UDC: 536.25+517.958
MSC: Primary 76D05, 76E15; Secondary 35K05
Received: 23.02.1993

Citation: V. I. Yudovich, “Linear stability of equilibria of a fluid that is a nonconductor of heat”, Mat. Sb., 185:5 (1994), 139–159; Russian Acad. Sci. Sb. Math., 82:1 (1995), 117–134

Citation in format AMSBIB
\Bibitem{Yud94}
\by V.~I.~Yudovich
\paper Linear stability of equilibria of a~fluid that is a~nonconductor of heat
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 5
\pages 139--159
\mathnet{http://mi.mathnet.ru/msb900}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1275975}
\zmath{https://zbmath.org/?q=an:0841.76021}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 1
\pages 117--134
\crossref{https://doi.org/10.1070/SM1995v082n01ABEH003555}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RR54800006}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Tsybulin V., Yudovich V., “Invariant Sets and Attractors of Quadratic Mapping of Plane: Computer Experiment and Analytical Treatment”, J. Differ. Equ. Appl., 4:5 (1998), 397–423  crossref  mathscinet  zmath  isi
    2. V. I. Yudovich, “Convection of a very viscous and non-heat-conductive fluid”, Sb. Math., 198:1 (2007), 117–146  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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