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AIMS Mathematics

2018, Volume 3, Issue 4: 565-574. doi: 10.3934/Math.2018.4.565
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Research article

A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations

  • 1.
    ENS of Mostaganem, University of Mostaganem, Box 227, Mostaganem 27000, Algeria
  • 2.
    Dipartimento di Matematica e Informatica, Università di Catania, Viale Andrea Doria, 6 95125 Catania - Italy
  • 3.
    RUDN University, 6 Miklukho - Maklay St, Moscow, 117198, Russia
  • 4.
    Department of Mathematical Science, Faculty of Applied Science, Umm Alqura University, P. O. Box 14035, Makkah 21955, Saudi Arabia
  • Published: 28 November 2018
  • In this work, we investigate the regularity criterion for the solution of the Hall-MHD system in three-dimensions. It is proved that if the pressure $\pi $ and the gradient of magnetic field $ \nabla B$ satisfies some kind of space-time integrable condition on $[0, T]$, then the corresponding solution keeps smoothness up to time T. This result improves some previous works to the Morrey space $\overset{\cdot }{\mathcal{M }}_{2, \frac{3}{r}}$ for $0\leq r \lt 1$ which is larger than $L^{\frac{3}{r}}$.

    Citation: A. M. Alghamdi, S. Gala, M. A. Ragusa. A regularity criterion of smooth solution for the 3D viscous Hall-MHD equations[J]. AIMS Mathematics, 2018, 3(4): 565-574. doi: 10.3934/Math.2018.4.565

    Related Papers:

  • In this work, we investigate the regularity criterion for the solution of the Hall-MHD system in three-dimensions. It is proved that if the pressure $\pi $ and the gradient of magnetic field $ \nabla B$ satisfies some kind of space-time integrable condition on $[0, T]$, then the corresponding solution keeps smoothness up to time T. This result improves some previous works to the Morrey space $\overset{\cdot }{\mathcal{M }}_{2, \frac{3}{r}}$ for $0\leq r \lt 1$ which is larger than $L^{\frac{3}{r}}$.


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