  In this paper we initiate the mathematical analysis of a system of nonlinear
Stochastic Partial Differential equations describing the motion of turbulent
Non-Newtonian media in the presence of fluctuating magnetic field. The system
is basically obtained by a coupling of the dynamical equations of a
Non-Newtonian fluids having $p$-structure and the Maxwell equations. We mainly
show the existence of weak martingale solutions and their exponential decay
when time goes to infinity.

Analysis of PDEs