Dynamic Bifurcation Theory of Rayleigh-bénard Convection with Infinite Prandtl Number

We study in this paper the bifurcation and stability of the solutions of the Rayleigh-Bénard convection which has the infinite Prandtl number, using a notion of bifurcation called attractor bifurcation. We prove that the problem bifurcates from the trivial solution to an attractor AR when the Rayleigh number R crosses the first critical Rayleigh number Rc. As a special case, we also prove another result which corresponds to the classical pitchfork bifurcation, that this bifurcated attractor AR consists of only two stable steady states when the first eigenvalue R1 is simple.