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Homogenization of Trajectory Statistical Solutions for the 3D Incompressible Micropolar Fluids with Rapidly Oscillating Terms

Author

Listed:
  • Hujun Yang

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

  • Xiaoling Han

    (Department of Mathematics, Northwest Normal University, Lanzhou 730070, China)

  • Caidi Zhao

    (Department of Mathematics, Wenzhou University, Wenzhou 325035, China)

Abstract

This article studies the 3D incompressible micropolar fluids with rapidly oscillating terms. The authors prove that the trajectory statistical solutions of the oscillating fluids converge to that of the homogenized fluids provided that the oscillating external force and angular momentum possess some weak homogenization. The results obtained indicate that the trajectory statistical information of the 3D incompressible micropolar fluids has a certain homogenization effect with respect to spatial variables. In addition, our approach is also valid for a broad class of evolutionary equations displaying the property of global existence of weak solutions without a known result of global uniqueness, including some model hydrodynamic equations, MHD equations and non-Newtonian fluids equations.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2469-:d:863768
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    References listed on IDEAS

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    1. Zhao, Caidi & Jiang, Huite & Caraballo, Tomás, 2021. "Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices," Applied Mathematics and Computation, Elsevier, vol. 404(C).
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    Cited by:

    1. 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.

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