Abstract
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
\(\underset{0}{\overset{T}{\int }}\left({\Vert \nabla \pi \left(t\right)\Vert }_{{\dot{B}}_{\infty ,\infty }^{0}}^\frac{2}{3}+{\Vert \nabla B\left(t\right)\Vert }_{BMO}^{2}\right)dt<\infty ,\)
which can be regarded as improvement of the result in [3].
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 67, No. 3, In honor of the 70th anniversary of Professor V. M. Filippov, 2021.
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Gala, S., Ragusa, M.A. An Improved Blow-Up Criterion for the Magnetohydrodynamics with the Hall and Ion-Slip Effects. J Math Sci 278, 306–313 (2024). https://doi.org/10.1007/s10958-024-06921-8
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DOI: https://doi.org/10.1007/s10958-024-06921-8