Global regularity for 2D magneto-micropolar equations with only micro-rotational velocity dissipation and magnetic diffusion.

This paper studies the global regularity of classical solutions to 2D magneto-micropolar fluid equations with only micro-rotational velocity dissipation and magnetic diffusion. Here the micro-rotational velocity dissipation and magnetic diffusion are given by − Δ Ω and ( − Δ ) β b . Making use of several combined quantities, maximal regularity of heat operator and Littlewood–Paley decomposition theory, we establish a regularity criterion in terms of magnetic field for the case β = 1 and the global regularity for β > 1 . The regularity criterion given here is also new even for the 2D magnetohydrodynamic equations. In addition, to prove these two main results, as preparation we establish a new global a priori estimate for magnetic field, namely Δ b ∈ L ∞ ( 0 , T ; L p ( R 2 ) ) with p ≥ 2 which also holds for the 2D magnetohydrodynamic equations as a particular case. [ABSTRACT FROM AUTHOR]