Global regularity for the 2D magneto‐micropolar system with partial and fractional dissipation

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 if the initial data is sufficiently smooth. In addition, we also obtained the global regularity results for several partial dissipation cases.