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March  2010, 28(1): 99-130. doi: 10.3934/dcds.2010.28.99

Rotating Boussinesq equations: Dynamic stability and transitions

Chun-Hsiung Hsia 1, , Tian Ma 2, and  Shouhong Wang 3,

1. 

Department of Mathematics, National Taiwan University, Taipei, 10617, Taiwan
2. 

Department of Mathematics, Sichuan University, Chengdu
3. 

Department of Mathematics, Indiana University, Bloomington, IN 47405

Received  September 2009 Revised  February 2010 Published  April 2010

The main objective of this article is to study dynamic transitions and stability for rotating incompressible flows, governed by the rotating Boussinesq equations. It is proved that there are only two types of transitions, Type-I (continuous) and Type-II (jump) transitions, as the Rayleigh number crosses the first real or complex eigenvalues. Specific criteria are given to determine the type of transitions as well.
Keywords: dynamic transition theory, geophysical fluid dynamics, jump transition, periodic solutions., continuous transition, singularity separation, Rotating Boussinesq equations.
Mathematics Subject Classification: 86A10, 76U05, 76E, 35Q35, 37.
Citation: Chun-Hsiung Hsia, Tian Ma, Shouhong Wang. Rotating Boussinesq equations: Dynamic stability and transitions. Discrete & Continuous Dynamical Systems - A, 2010, 28 (1) : 99-130. doi: 10.3934/dcds.2010.28.99
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