Asymptotic behavior of a system of micropolar equations
Pedro Marín-Rubio, Mariano Poblete-Cantellano, Marko Antonio Rojas-Medar, Francisco J. Torres · Electronic journal of qualitative theory of differential equations · 2016
This work is concerned with three-dimensional micropolar fluids flows in a bounded domain with boundary of class $C^{\infty}.$ Based on the theory of dissipative systems, we prove the existence of a restricted global attractors for local semiflows on suitable fractional phase spaces $\mathbf{Z}^{\alpha}_{p},$ namely for $p\in (3,+\infty)$ and $\alpha\in [1/2,1)$. Moreover, we prove that all these attractors are in fact the same set. Previously, it is shown that the Lamé operator is a sectorial operator in each $L_{p}(\Omega)$ with $1<p<+\infty$, $p eq 3/2$ and therefore, it generates an analytic semigroup in these spaces.