Dynamic Transition for Magnetohydrodynamic Convection

Details Dynamic Transition for Magnetohydrodynamic Convection Dynamic Transition for Magnetohydrodynamic Convection

2010-05-18

arxiv.org/abs/1005.3218v2

Mathematics

Analysis of PDEs

This article is replaced by a newer version. See arXiv:1105.0964v1

Scientific paper

Main objective of this paper is to describe the dynamic transition of the incompressible MHD equations in a rectangular domain in $\mathbb{R}^{3}$. Our analysis shows that the system undergoes a first dynamic transition either to multiple equilibria or to periodic solutions. In the case of transition to multiple equilibria, the transition is a type-I (continuous) transition. In the case of transition to periodic solutions, the transition can be either type-I or type-II (jump).

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