Global wellposedness of magnetohydrodynamics for Boussinesq system with partial viscosity and zero magnetic diffusion

This paper is concerned with the initial boundary value problem of the two-dimensional partial viscosity incompressible magneto-hydrodynamics-Boussinesq system with zero magnetic diffusion in a strip domain. A unique global strong solution with small initial data is established, which is around the equilibrium state (0,0,e1) for Navier slip boundary condition on velocity. This is an extension of Ren-Xiang-Zhang's result (Ren et al., 2016, [24]). However, we just need the sum of ‖u1‖L2+‖∂2u‖L2+‖Δu‖L2, ‖∂2θ‖L2+‖∂12θ‖L2 and ‖b1‖L2+‖∂2b‖L2+‖Δb‖L2 is suitable small at initial time.