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

Jingbo Wu (), Qing-Qing Wang and Tian-Fang Zou
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Jingbo Wu: College of Physics and Optoelectronic Engineering, Shenzhen University, Shenzhen 518060, China
Qing-Qing Wang: College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
Tian-Fang Zou: Department of Mathematics, Wenzhou University, Wenzhou 325035, China

Mathematics, 2023, vol. 11, issue 10, 1-14

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 ∥ L 2 + ∥ ∇ u ∥ L 2 ≤ C ( 1 + t ) − 3 2 and ∥ u ∥ L 2 ≤ C ( 1 + t ) − 3 2 , ∥ ω ∥ L 2 ≤ 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.

Keywords: 2D micropolar fluid; angular viscosity dissipation; large time decay (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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