Long-time behavior of micropolar fluid equations in cylindrical domains

In this paper we investigate the existence of the H1H1-uniform attractor and long-time behavior of solutions to non-autonomous micropolar fluid equations in three dimensional cylindrical domains. In our considerations we take into account that the existence of global and strong solutions is proved under the assumption on smallness of change of the initial and the external data along the axis of the cylinder. Therefore, we refine the concept of the uniform attractor by adopting the idea which was proposed by J.W. Cholewa and T. Dłotko (1998) in [9].