The regularity criteria on the magnetic field to the $3D$ incompressible MHD equations

Improved blow up criterion for the three dimensional incompressible magnetohydrodynamics system

“…On the other hand, there exist a vast literature on finite time blowup or nonblowup criteria for local strong solutions. By discovering some special structures of the nonlinear coupling terms with the magnetic field, the authors of [13,21,23,24,25,26,27] were able to provide us some regularity criteria involving lesser components of the velocity field and the magnetic field.…”