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In this article we initiate the mathematical study of the dynamics of asystem of nonlinear Partial Differential Equations modelling the motion ofincompressible, isothermal and conducting modified bipolar fluids in presenceof magnetic field. We mainly prove the existence of weak solutions to themodel. We also prove the existence of a trajectory attractor to the translationsemigroup acting on the trajectories of the set of weak solutions and that ofexternal forces. Some results concerning the structure of this trajectoryattractor are also given. The results from this paper may be useful in theinvestigation of some system of PDEs arising from the coupling ofincompressible fluids of $p$-structure and the Maxwell equations.

Trajectory attractor for a non-autonomous Magnetohydrodynamic equations of Non-Newtonian Fluids