Remark on an improved regularity criterion for the 3D MHD equations

In this paper we investigate the regularity criterion for the local in time classical solution to the 3D incompressible magnetohydrodynamic equations. We prove that if ∇×u∇×u belongs to L2(0,T;Ḃ∞,∞−1), then the local solution (u,B) can be extended beyond time TT. As a consequence, this result extends several previous works.