Non blow-up criterion for the 3-D Magneto-hydrodynamics equations in the limiting case

In this paper, we prove that suitable weak solution (u, b) of the 3-D MHD equations can be extended beyond T if u ∈ L^∞(0, T;L³(R³)) and the horizontal components b_h of the magnetic field satisfies the well-known Ladyzhenskaya-Prodi-Serrin condition, which improves the corresponding regularity criterion by Mahalov-Nicolaenko-Shilkin.