Sharp decay estimates for 3D incompressible MHD system with mixed partial dissipation and magnetic diffusion

This paper focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed partial dissipation and magnetic diffusion. By using the energy methods, we obtain that this system possesses a global solution when the initial data is small in H3(R3). In addition, the optimal decay rates of this global solution and its first-order derivatives are established by bounding two time-weighted norms and applying a bootstrapping argument.