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Bifurcation of infinite Prandtl number rotating convection
Authors:Jungho Park
Institution:Department of Mathematics, New York Institute of Technology, Old Westbury, NY 11568, United States
Abstract:We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park (2005, 2007, revised for publication) 5], 6] and 25] under various boundary conditions. By thoroughly investigating we prove in this paper that the solutions bifurcate from the trivial solution u=0 to an attractor ΣR which consists of only one cycle of steady state solutions and is homeomorphic to S1. We also see how intensively the rotation inhibits the onset of convective motion. This bifurcation analysis is based on a new notion of bifurcation, called attractor bifurcation which was developed by Ma and Wang (2005); see 15].
Keywords:35Q  35B  37L  76E  76U
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