Dynamic bifurcation theory of Rayleigh-Bénard convection with infinite Prandtl number (Q2496598)

The author investigates the fluid motion induced by different heating of a layer of fluid bounded by two horizontal parallel plates at a distance \(h_a\), -- the Rayleigh-Bénard convection -- modeled by the infinite Prandtl number limit of the Boussinesq equation (model for mantle convection in terrestrial geophysics). The new bifurcation theory based on the notion ``attractor bifurcation'' [\textit{T. Ma, S. Wang}, Bifurcation theory and applications, Hackensack, NJ: World Scientific. (2005; Zbl 1085.35001)] is applied to the considered problem. It is proved that the problem bifurcates from the trivial solution to an attractor \(\mathcal{A}_R\) when the Rayleigh number \(R\) crosses its critical value \(R_c\). When the first eigenvalue \(R_1\) is simple this bifurcated attractor \(\mathcal{A}_R\) consists of only two steady states.