On the 3-D stochastic magnetohydrodynamic-α model

Abstract

We consider the stochastic three dimensional magnetohydrodynamic-α model (MHD-α) which arises in the modeling of turbulent flows of fluids and magnetofluids. We introduce a suitable notion of weak martingale solution and prove its existence. We also discuss the relation of the stochastic 3D MHD-α model to the stochastic 3D magnetohydrodynamic equations by proving a convergence theorem, that is, as the length scale α tends to zero, a subsequence of weak martingale solutions of the stochastic 3D MHD-α model converges to a certain weak martingale solution of the stochastic 3D magnetohydrodynamic equations. Finally, we prove the existence and uniqueness of the probabilistic strong solution of the 3D MHD-α under strong assumptions on the external forces.