Improved decay results for micropolar flows with nonlinear damping

Abstract

We examine the long-time behavior of solutions (and their derivatives) to the micropolar equations with nonlinear velocity damping. Additionally, we get a speed-up gain of $t^{1/2}$ for the angular velocity, consistent with established findings for classic micropolar flows lacking nonlinear damping. Consequently, we also obtain a sharper result regarding the asymptotic stability of the micro-rotational velocity $w(\cdot ,t)$. Related results of independent interest are also included.