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).
Categories: math.AP physics.flu-dyn