THE GLOBAL L2 STABILITY OF SOLUTIONS TO THREE DIMENSIONAL MHD EQUATIONS∗

Abstract In this paper, we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains. Under suitable conditions of the large solutions, it is shown that the large solutions are stable. And we obtain the equivalent condition of this stability condition. Moreover, the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established. Key words MHD equations; strong solutions; stability 2010 MR Subject Classification 35Q35; 76B03