Dynamic Transition for Magnetohydrodynamic Convection

Abstract

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).

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