On the Dynamics of Controlled Magnetohydrodynamic Systems

摘要: In this paper we study the long time behavior of solutions for an optimal control problem associated with viscous incompressible electrically conducting fluid modeled by magnetohydrodynamic (MHD) equations in a bounded two dimensional domain through adjustment distributed controls. We first con struct quasi-optimal solution MHD systems which possesses exponential decay time. then derive some preliminary estimates long-time all admissible systems. Next prove existence both finite and infinite intervals. Finally, establis h properties problem.