LAUSR

This paper focuses on the 2D incompressible magneto‐micropolar sysytem with the kinematic dissipation given by the fractional operator (−Δ)α, the magnetic diffusion by the fractional operator (−Δ)β and the spin dissipation by the fractional operator (−Δ)γ. α,β, and γ are nonnegative constants. We proved that this system with any α+β=2,1 ≤ α ≤ 2,γ=0, and α+γ ≥ 1,β=1 always possesses a unique global smooth solution (u,b,w)∈Hs(R2)(s>2) if the initial data is sufficiently smooth. In addition, we also obtained the global regularity results for several partial dissipation cases.