The exponential behavior and stabilizability of a stochastic 3D magnetohydrodynamic – Alpha model with cylindrical multiplicative noise

Abstract

We study in this article, a stochastic evolution equation for the motion of magneto-fluid filling a periodic domain of : The existence and uniqueness of stationary solution is established and the long time behavior of solution is studied. The proof relies on a Galerkin approximation. Mainly, we prove that under some conditions on the forcing terms, the variational solution converges exponentially in the mean square and almost surely exponentially to the stationary solution. We also prove a result related to the stabilization of the model.