Paul Andre Razafimandimby
Published 2011-11-12, updated 2012-06-22Version 4
In this article we initiate the mathematical study of the dynamics of a system of nonlinear Partial Differential Equations modelling the motion of incompressible, isothermal and conducting modified bipolar fluids in presence of magnetic field. We mainly prove the existence of weak solutions to the model. We also prove the existence of a trajectory attractor to the translation semigroup acting on the trajectories of the set of weak solutions and that of external forces. Some results concerning the structure of this trajectory attractor are also given. The results from this paper may be useful in the investigation of some system of PDEs arising from the coupling of incompressible fluids of $p$-structure and the Maxwell equations.
A note about existence for a class of viscous fluid problems
On the regularity of weak solutions of the 3D Navier-Stokes equations in $B^{-1}_{\infty,\infty}$
Existence of steady solutions of Newtonian and Non-Newtonian fluids with right hand sides beyond duality
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