We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of Chemin and Zhang  and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.
- Anisotropic Littlewood–Paley theory
- Global regularity
- Magnetohydrodynamics system
- Navier–Stokes equations