Global well-posedness for MHD system with mixed partial dissipation and magnetic diffusion in 212 dimensions

摘要

This paper concentrates on the global well-posedness for 212D incompressible Magnetohydrodynamic (MHD) system with mixed partial dissipation and magnetic diffusion. For 212D MHD flows with full dissipation and magnetic diffusion terms, the global existence and uniqueness can be obtained by the standard energy method. However, can the classical solutions for incompressible MHD flows in 212 dimensions keep its global regularity losing some partial dissipation and magnetic diffusion terms? We will give a rigorous proof to the global well-posedness for the 212D MHD flows with the mixed partial dissipation and magnetic diffusion case in this paper.