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; L (ℝ)) and the horizontal components b of the magnetic field satisfies the well-known Ladyzhenskaya-Prodi-Serrin condition, which improves the corresponding regularity criterion by Mahalov-Nicolaenko-Shilkin. [ABSTRACT FROM AUTHOR]