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

Abstract

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.