Global existence of three-dimensional incompressible magneto-micropolar system with mixed partial dissipation, magnetic diffusion and angular 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 strong solution of magneto-micropolar equations in three-dimensional can exist globally in time with large initial data is still unknown. In this paper, we deal with the Cauchy problem of the three-dimensional magneto-micropolar system with mixed partial dissipation, magnetic diffusion and angular viscosity. More precisely, the global existence of smooth solutions to the three-dimensional incompressible magneto-micropolar fluid equations with mixed partial dissipation, magnetic diffusion and angular viscosity are obtained by energy method under the assumption that H1-norm of the initial data (u0,b0,w0) sufficiently small, namely ‖u0,b0,ω0‖H1(R3)2≤ε2, where ε is a sufficiently small positive number. This work follows the techniques in the paper of Cao and Wu (2011).