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

In this work, we consider the magnetohydrodynamics system with the Hall and ion-slip effects in ℝ3. The main result is a sufficient condition for regularity on a time interval [0, T] expressed in terms of the norm of the homogeneous Besov space $${\dot{B}}_{\infty ,\infty }^{0}$$ with respect to the pressure and the BMO−norm with respect to the gradient of the magnetic field, respectively $$\underset{0}{\overset{T}{\int }}\left({\Vert abla \pi \left(t\right)\Vert }_{{\dot{B}}_{\infty ,\infty }^{0}}^\frac{2}{3}+{\Vert abla B\left(t\right)\Vert }_{BMO}^{2}\right)dt<\infty ,$$ which can be regarded as improvement of the result in [3].