On Selective Decay States of 2D Magnetohydrodynamic Flows

Abstract

The selective decay phenomena has been observed by physicists for many dynamic flows such as Navier-Stoke flows, barotropic geophysical flows, and magnetohydrodynamic (MHD) flows in either actual physical experiments or numerical simulations. Rigorous mathematical works have been carried out for both Navier-Stoke and barotropic geophysical flows. In our previous work, we have rigorously showed the existence of selective states for 2D MHD flows. In this paper, we present a partial result on instability of the selective states.