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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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