Asymptotic behavior of weak and strong solutions of the magnetohydrodynamic equations

We prove some results on the stability of slow stationary solutions of the MHD equations in two- and three-dimensional bounded domains for external force fields that are asymptotically autonomous. Our results show that weak solutions are asymptotically stable in time in the $ L^2 $-norm. Further, assuming certain regularity hypotheses on the problem data, strong solutions are asymptotically stable in the $ H^1 $ and $ H^2 $-norms.