Geodesic
An improved blow-up criterion for the magnetohydrodynamics with the Hall and ion-slip effects
Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 526-534 
S. Gala; M. A. Ragusa. An improved blow-up criterion for the magnetohydrodynamics with the Hall and ion-slip effects. Contemporary Mathematics. Fundamental Directions, Dedicated to 70th anniversary of the President of the RUDN University V. M. Filippov, Tome 67 (2021) no. 3, pp. 526-534. http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a7/
@article{CMFD_2021_67_3_a7,
     author = {S. Gala and M. A. Ragusa},
     title = {An improved blow-up criterion for the magnetohydrodynamics with the {Hall} and ion-slip effects},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {526--534},
     year = {2021},
     volume = {67},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2021_67_3_a7/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

In this work, we consider the magnetohydrodynamics system with the Hall and ion-slip effects in $\mathbb{R}^{3}$. 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 \begin{equation*} \int_{0}^{T}\left( \left\Vert \nabla \pi (t)\right\Vert _{\dot{B}_{\infty ,\infty }^{0}}^{\frac{2}{3}}+\left\Vert \nabla B(t)\right\Vert _{BMO}^{2}\right) dt\infty , \end{equation*} which can be regarded as improvement of the result in [3].

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