Optimal time decay rates of solutions for the 2D generalized
magneto-micropolar equations
Abstract
This study is concerned with the optimal time rates of weak solutions
for the 2D magneto-micropolar equations with only micro-rotational
dissipation and magnetic diffusion. Due to some new observations, we
obtain the optimal time decay rates of weak solutions
$\|\nabla
u(t)\|_{L^2}+\|\nabla
w(t)\|_{L^2}\le
C(1+t)^{-2}$ and $
\|\nabla
b(t)\|_{L^{p}}\le
C(1+t)^{-\frac12-(1-\frac1p)}$ with
$p\in[2,\infty)$.