@article{Guo2025, 
author = {Yana Guo and Chaoying Li},
title = {Large-time behavior of solutions to the 2D generalized magneto-micropolar equations},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {12},
pages = {7551-7569},
keywords = {magneto-micropolar equations, decay rates, fractional magnetic dissipation, linear velocity damping, Hardy-Littlewood-Sobolev inequality},
url = {https://www.sciopen.com/article/10.3934/era.2025333},
doi = {10.3934/era.2025333},
abstract = {This work provides rigorous verification of the super-smoothing effect of higher-order fractional Laplacian dissipation. Shang and Zhao (2017) have proved the global regularity of classical solutions of the 2D incompressible magneto-micropolar equations with linear velocity damping    u, microrotational dissipation    (  −  Δ  )  ω, and magnetic diffusion    (  −  Δ      )    β    b  ,  β  >  1. This paper is devoted to further investigating the large-time behavior of global smooth solutions of the system with    1  <  β  ≤      3    2  . We apply the negative Sobolev space to overcome the difficulty caused by fractional-order dissipation and establish        ∫          0              t        ‖  ∇  b  (  τ  )      ‖                  L                  2                      d  τ  ≤  C. Furthermore, by fully exploiting the special structure of the system and combining the properties of a heat operator with the generalized Fourier splitting methods, we obtain the decay rates of the solutions and their first-order derivatives for    1  ≤  p  ≤      2    β  .}
}