Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping

Abstract

This paper studies the large time behavior of solutions to the 2D micropolar equations with linear damping velocity. It is proven that the global solutions have rapid time decay rates ∥∇ω∥L2+∥∇u∥L2≤C(1+t)−32 and ∥u∥L2≤C(1+t)−32,∥ω∥L2≤C(1+t)−1. The findings are mainly based on the new observation that linear damping actually improves the low-frequency effect of the system. The methods here are also available for complex fluid models with linear damping structures.