Abstract
The selective decay phenomena has been observed by physicists for many dynamic flows such as Navier–Stokes 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–Stokes and barotropic geophysical flows. It is the goal of this paper to verify the selective decay principle mathematically for the 2D magnetohydrodynamic (MHD) flows.