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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jingbo Wu & Qing-Qing Wang & Tian-Fang Zou, 2023. "Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping," Mathematics, MDPI, vol. 11(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2311-:d:1147763
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    References listed on IDEAS

    as
    1. Zhao, Caidi & Li, Bei, 2017. "Time decay rate of weak solutions to the generalized MHD equations in R2," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 1-8.
    2. Hujun Yang & Xiaoling Han & Caidi Zhao, 2022. "Homogenization of Trajectory Statistical Solutions for the 3D Incompressible Micropolar Fluids with Rapidly Oscillating Terms," Mathematics, MDPI, vol. 10(14), pages 1-15, July.
    3. Zhao, Caidi & Zhu, Hongjin, 2015. "Upper bound of decay rate for solutions to the Navier–Stokes–Voigt equations in R3," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 183-191.
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    2. Zhao, Caidi & Li, Bei, 2017. "Time decay rate of weak solutions to the generalized MHD equations in R2," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 1-8.

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