On existence, uniqueness and Lr-exponential stability for stationary solutions to the MHD equations in three-dimensional domains

Abstract The existence of stationary solutions to the MHD equations in three-dimensional bounded domains will be proved. At the same time if the assumption of smallness is made on external forces, uniqueness of the stationary solutions can be guaranteed and it can be shown that any L r ( r > 3) global bounded non-stationary solution to the MHD equations approaches the stationary solution under both L 2 and L r norms exponentially as time goes to infinity.