Research article

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

  • Received: 20 August 2018 Accepted: 20 October 2018 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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