Some qualitative properties of the solutions of the Magnetohydrodynamic equations for nonlinear bipolar fluids
arXiv:1206.1169 · doi:10.1007/s10440-014-9964-2
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 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.
arXiv commentThe final publication is available at Springer via http://dx.doi.org/10.1007/s10440-014-9964-2