Abstract
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.
Citation
B. Scarpellini. "Equilibrium solutions of the Bénard equations with an exterior force." Differential Integral Equations 16 (2) 129 - 158, 2003. https://doi.org/10.57262/die/1356060681
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