Asymptotic behaviour of a system of micropolar equations

Abstract

This work is concerned with three-dimensional micropolar fluids flows in a bounded domain with boundary of class C∞. Based on the theory of dissipative systems, we prove the existence of restricted global attractors for local semiflows on suitable fractional phase spaces Z αp, namely for p ∈ (3, +∞) and α ∈ [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 Lp(Ω) with 1 < p < +∞, p 6= 3/2 and therefore, it generates an analytic semigroup in these spaces.