Beale-kato-majda’s criterion for magneto-hydrodynamic equations with zero viscosity

This paper is concerned with studying the blow-up criterion of smooth solutions to the three dimensional magneto-hydrodynamic equations with zero viscosity. We prove that the smooth solution may be extended by standard energy method, provided the norm of the gradient of velocity in a space much bigger than Ḃ0∞,∞. The result obtained in this manuscript improves the former corresponding result. © 2020, Institute of Mathematics. All rights reserved.