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arXiv · 1206.1169

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

Paul Andre Razafimandimby
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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.

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Paul Andre Razafimandimby. 2012-06-06. Some qualitative properties of the solutions of the Magnetohydrodynamic equations for nonlinear bipolar fluids. https://doi.org/10.1007/s10440-014-9964-2

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