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In this article we study the long-time behaviour of a system of nonlinearPartial Differential Equations (PDEs) modelling the motion of incompressible,isothermal and conducting modified bipolar fluids in presence of magneticfield. We mainly prove the existence of a global attractor denoted by $\A$ forthe nonlinear semigroup associated to the aforementioned systems of nonlinearPDEs. We also show that this nonlinear semigroup is uniformly differentiable on$\A$. This fact enables us to go further and prove that the attractor $\A$ isof finite-dimensional and we give an explicit bounds for its Hausdorff andfractal dimensions.

Some qualitative properties of the solutions of the Magnetohydrodynamic equations for nonlinear bipolar fluids