caa a22 4500 606166041 CHVBK 20210128100656.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s10440-014-9964-2 doi (NATIONALLICENCE)springer-10.1007/s10440-014-9964-2 Razafimandimby Paul Department of Mathematics and Information Technology, Montanuniversität Leoben, Franz Josef Strasse 18, 8700, Leoben, Austria aut Some Qualitative Properties of the Solution to the Magnetohydrodynamic Equations for Nonlinear Bipolar Fluids [Elektronische Daten] [Paul Razafimandimby] 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 $\mathcal{A}$ for the semigroup associated to the aforementioned system of nonlinear PDEs. We also show that this semigroup is uniformly differentiable on $\mathcal{A}$ . This fact enables us to go further and prove that the attractor $\mathcal{A}$ is of finite-dimensional and we give an explicit bounds for its Hausdorff and fractal dimensions. Springer Science+Business Media Dordrecht, 2014 Non-Newtonian fluids nationallicence Bipolar fluids nationallicence Shear thinning fluids nationallicence MHD nationallicence Magnetohydrodynamics nationallicence Asymptotic behavior nationallicence Long-time behavior nationallicence Global attractor nationallicence Hausdorff dimension nationallicence Fractal dimension nationallicence Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 213-240 0167-8019 138:1<213 2015 138 10440 https://doi.org/10.1007/s10440-014-9964-2 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9964-2 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Razafimandimby Paul Department of Mathematics and Information Technology, Montanuniversität Leoben, Franz Josef Strasse 18, 8700, Leoben, Austria aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 138/1(2015-08-01), 213-240 0167-8019 138:1<213 2015 138 10440