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May  2010, 13(3): 577-591. doi: 10.3934/dcdsb.2010.13.577

Three-dimensional sphere $S^3$-attractors in Rayleigh-Bénard convection

1. 

Department of Mathematics, Sichuan University, Chengdu 610064, China

Received  October 2008 Revised  January 2010 Published  February 2010

The main objective of this article is to study dynamic of the three-dimensional Boussinesq equations with the periodic boundary condition.We prove that when the Rayleigh number $R$ crosses the first critical Rayleigh number $R_c$, the Rayleigh-Bénard problem bifurcates from the basic state to an global attractor $\Sigma$, which is homeomorphic to $S^3$.
Citation: Tingyuan Deng. Three-dimensional sphere $S^3$-attractors in Rayleigh-Bénard convection. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 577-591. doi: 10.3934/dcdsb.2010.13.577
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