Long-time behavior of micropolar fluid equations in cylindrical domains

TL;DR

This paper studies the long-term dynamics and existence of uniform attractors for non-autonomous micropolar fluid equations in cylindrical domains, considering the impact of small data variations along the cylinder axis.

Contribution

It refines the concept of uniform attractors for micropolar fluids by incorporating smallness conditions on data changes along the cylinder axis.

Findings

Existence of $H^1$-uniform attractor established.

Long-time behavior characterized under small data variation assumptions.

Refined attractor concept applicable to non-autonomous micropolar fluids.

Abstract

In this paper we investigate the existence of $H^1$-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 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 uniform attractor by adopting the idea which was proposed by J.W. Cholewa and T. D{\l}otko in \cite{chol1}.