Beale-Kato-Majda's criterion for magneto-hydrodynamic equations with zero viscosity


Ahmad M. Alghamdi, Sadek Gaka, Maria Alessandra Ragusa




This paper is concerned to study 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 that the norm of the gradient of velocity in a space much bigger than $\overset{.}{B}_{\infty ,\infty }^{0}$. This result obtained in this manuscript improves the former corresponding result.