In this talk, we will discuss the decay results on a 2D magnetohydrodynamic (MHD) system with only vertical dissipation or horizontal dissipation. For vertical dissipation, we show that the H^2-norm of any perturbation near a background magnetic field actually decays algebraically in time. Mathematically this result along with its proof offers a new and effective approach to the large-time behavior on partially dissipated systems. For horizontal dissipation, we show the stability result on the perturbations near a background magnetic field. In addition, the solution converges to its horizontal average asymptotically.

https://arizona.zoom.us/j/82763762677