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

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 modified bipolar fluids in presence of magnetic field. We mainly prove the existence of a global attractor denoted by \A for the nonlinear semigroup associated to the aforementioned systems of nonlinear PDEs. 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 is of finite-dimensional and we give an explicit bounds for its Hausdorff and fractal dimensions.Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s10440-014-9964-

On the exponential behaviour of stochastic evolution equations for non-Newtonian fluids

We investigate the exponential long-time behaviour of the stochastic evolution equations describing the motion of a non-Newtonian fluids excited by multiplicative noise. Some results on the exponential convergence in mean square and with probability one of the weak probabilistic solution to the stationary solutions are given. We also prove an interesting result related to the stabilization of these stochastic evolution equations.The University of Pretoria and the National Research Foundation South Africa.http://www.tandfonline.com/loi/gapa20hb2016Mathematics and Applied Mathematic