L2− asymptotic stability of the mild solution to the 3D MHD equation

In this paper, we investigate the L2− asymptotic stability of a global-in-time mild solution of the small initial value problem to the 3D magnetohydrodynamic (MHD) equations. We construct a weak solution to the MHD equation, and then we show this weak solution converges to the mild solution in the sense of L2 energy norm.