Some Qualitative Properties of the Solution to the Magnetohydrodynamic Equations for Nonlinear Bipolar Fluids

Abstract

Abstract. In this article we study the long-time behaviour of a system of nonlinear Partial Differential Equations (PDEs) modelling the motion of incompressible, isothermal and conducting bipolar fluids in presence of magnetic field. We mainly prove the existence of a global attractor denoted by A for the semigroup associated to the aforementioned systems of nonlinear PDEs. We also show that this semigroup is uniformly differentiable on A. This fact enables us to go further and prove that the attractor A is of finitedimensional and we give an explicit bounds for its Hausdorff and fractal dimensions.