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

Abstract

In this paper, we prove that suitable weak solution $(u,b)$ of the 3-D MHD equations can be extended beyond $T$ if $u\in L^{\infty }(0,T;L^3({\mathbb{R}}^3))$ and the horizontal components $b_h$ of the magnetic field satisfies the well-known Ladyzhenskaya-Prodi-Serrin condition.

References in corpus (2)

• On the regularity criterion of weak solution for the 3D viscous Magneto-hydrodynamics equations
• The Beale-Kato-Majda criterion to the 3D Magneto-hydrodynamics equations