Global regularity of the [formula omitted] magneto-micropolar fluid flows with partial magnetic diffusion

Abstract

In this paper, we studied the Cauchy problem of the magneto-micropolar fluid flows in 212 dimensions. If the initial data (u0,w0,b0)∈H2(R2), we obtain the global regularity of the 212D incompressible magneto-micropolar fluid flows with only horizontal magnetic diffusion or vertical magnetic diffusion. This work is inspired by the recent progresses made by Cao, etc., for 2D MHD equations with mixed partial dissipation and magnetic diffusion and Ji, etc., for 212D MHD system with mixed partial dissipation and magnetic diffusion.