A note on the regularity criterion for 3D MHD equations in Ḃ∞,∞-1 space

In this note, we consider sufficient conditions for the regularity of Leray Hoph Hopf solutions of the 3D incompressible magnetohydrodynamic equations via the velocity and magnetic fields in terms of Ḃ∞,∞-1 spaces. We prove that if (∇×u,∇×B)(∇×u,∇×B) belongs to the space L20,T;Ḃ∞,∞-1R3, then the solution (u,B)(u,B) is regular. This extends recent results contained in Gala (2011) [3].