@article{Song2024, 
author = {Xue-li Song and Yuan-yuan Liu and Xiao-tian Xie},
title = {The existence of uniform attractors for the 3D micropolar equations with nonlinear damping term},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {4},
pages = {9608-9630},
keywords = {uniform attractor, 3D micropolar equation, nonlinear damping term},
url = {https://www.sciopen.com/article/10.3934/math.2024470},
doi = {10.3934/math.2024470},
abstract = {This paper studies the existence of uniform attractors for 3D micropolar equation with damping term. When    β  >  3, with initial data    (      u          τ        ,      ω          τ        )  ∈      V          1        ×      V          2       and external forces    (      f          1        ,      f          2        )  ∈      H    (      f          1              0        )  ×      H    (      f          2              0        ), some uniform estimates of the solution in different function spaces are given. Based on these uniform estimates, the    (  (      V          1        ×      V          2        )  ×  (      H    (      f          1              0        )  ×      H    (      f          2              0        )  )  ,      V          1        ×      V          2        )-continuity of the family of processes    {      U          (              f                  1                    ,              f                  2                    )        (  t  ,  τ  )      }          t      ≥      τ       is demonstrated. Meanwhile, the    (      V          1        ×      V          2        ,            H        2    (  Ω  )  ×            H        2    (  Ω  )  )-uniform compactness of    {      U          (              f                  1                    ,              f                  2                    )        (  t  ,  τ  )      }          t      ≥      τ       is proved. Finally, the existence of a    (      V          1        ×      V          2        ,      V          1        ×      V          2        )-uniform attractor and a    (      V          1        ×      V          2        ,            H              2        (  Ω  )  ×            H              2        (  Ω  )  )-uniform attractor are obtained. Furthermore, the    (      V          1        ×      V          2        ,      V          1        ×      V          2        )-uniform attractor and the    (      V          1        ×      V          2        ,            H              2        (  Ω  )  ×            H              2        (  Ω  )  )-uniform attractor are verified to be the same.}
}