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2003 Equilibrium solutions of the Bénard equations with an exterior force
B. Scarpellini
Differential Integral Equations 16(2): 129-158 (2003).


In this paper we investigate questions of existence and uniqueness of equilibrium solutions of the inhomogeneous Bénard equations with exterior force $f$ which may be generated by a magnetic field which is not too strong. Two types of results are obtained. The first, based on a priori estimates and degree arguments states that there is a certain range $\lambda\leq \lambda_c+\delta_1$ for the Rayleigh parameter $\lambda$, for which existence can be asserted for any given force $f$, while the second result says that for $\lambda <\lambda_c$, $\lambda_c-\lambda$ small, there are forces $f$ which give rise to three different solutions. Here, $\lambda^2_c=R_c$ is the critical Rayleigh number which enters basically into our considerations.


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B. Scarpellini. "Equilibrium solutions of the Bénard equations with an exterior force." Differential Integral Equations 16 (2) 129 - 158, 2003.


Published: 2003
First available in Project Euclid: 21 December 2012

zbMATH: 1161.76469
MathSciNet: MR1947089

Primary: 76D05
Secondary: 35Q30 , 76E06 , 76W05

Rights: Copyright © 2003 Khayyam Publishing, Inc.


Vol.16 • No. 2 • 2003
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