On two-dimensional incompressible magneto-micropolar system with mixed partial viscosity

The magneto-micropolar fluid flows describe the motion of electrically conducting micropolar fluids in the presence of a magnetic field. The issue of whether the two-dimensional magneto-micropolar equations always possess a global (in time) classical solution can be difficult when there is only partial dissipation or no dissipation at all. In this paper, we deal with the Cauchy problem of the two-dimensional magneto-micropolar problem with mixed partial viscosity. More precisely, the global existence and regularity of classical solutions to the two-dimensional incompressible magneto-micropolar equations with mixed partial dissipation, magnetic diffusion and angular viscosity are obtained. Moreover, some conditional regularity of strong solutions is obtained for two-dimensional magneto-micropolar problem with mixed partial viscosity. This work is inspired by the recent work (Regmi and Wu, 2016) by Regmi and Wu, and our results extend their results to other mixed partial viscosities cases and global existence and regularity are established.