An Improved Blow-Up Criterion for the Magnetohydrodynamics with the Hall and Ion-Slip Effects

In this work, we consider the magnetohydrodynamics system with Hall and ion-slip effects in R3. The main result is a sufficient condition for regularity on time interval [0,T] expressed terms , of norm homogeneous Besov space B?,0{\dot{B}_{\infty,\infty}^0} respect to pressure BMO-norm gradient magnetic field, respectively
 ?0T(???(t)?B??,?02/3+??B(t)?BMO2)dt?{\int_{0}^{T} ({\| \Delta \pi(t)\|}^{2/3}_{\dot{B}_{\infty,\infty}^0} + {\| B (t)\|}^{2}_{BMO} ) dt