Global regularity for the 2D magneto-micropolar equations with partial and fractional dissipation

This paper studies two cases of global regularity problems on the 2D magneto-micropolar equations with partial magnetic diffusion and fractional dissipation. For the first case the velocity field is ideal, the micro-rotational velocity is with Laplacian dissipation and the magnetic field has fractional partial diffusion (-partial derivative(beta)(22)b(1), -partial derivative(beta)(11)b(2)) with beta > 1. In the second case, the velocity has a fractional Laplacian dissipation (-Delta)(alpha)u with any alpha > 0, the micro rotational velocity is with Laplacian dissipation and the magnetic field has partial diffusion (-partial derivative(22)b(1), -partial derivative(11)b(2)). In two cases the global well-posedness of classical solutions is proved in this paper. (C) 2018 Elsevier Ltd. All rights reserved.