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.
