Global Existence And Uniqueness Of Solutions For Three - Dimensional Magnetohydrodynamic Equations With Partially Dissipative

This article considers the existence of global smooth solutions to the Cauchy problem in3D incompressible magnetohydrodynamic(MHD) flows with mixed partial dissipation and magnetic diffusion. We prove that if the initial data sat-isfy‖u0‖H1+‖b0‖H1≤ε,where ε is a sufficiently small positive number, then the3D MHD equations with mixed partial dissipation and magnetic diffusion admit global unique smooth solutions.