Research article

A note on the Liouville type theorem for the smooth solutions of the stationary Hall-MHD system

  • Received: 25 May 2016 Accepted: 26 August 2016 Published: 13 October 2016
  • The main result of this work is to study the Liouville type theorem for the stationary Hall-MHD system on $\mathbb{R}.{3}$. Specificaly,we show that if $(u,B)$ is a smooth solutions to Hall-MHD equations satisfying $(u,B)\in L.%\frac{9}{2}(\mathbb{R}.3)$,then we have $u=B=0$. This improves a recent result of Chae et al. [2] and Zujin et al. [14].

    Citation: Sadek Gala. A note on the Liouville type theorem for the smooth solutions of the stationary Hall-MHD system[J]. AIMS Mathematics, 2016, 1(3): 282-287. doi: 10.3934/Math.2016.3.282

    Related Papers:

  • The main result of this work is to study the Liouville type theorem for the stationary Hall-MHD system on $\mathbb{R}.{3}$. Specificaly,we show that if $(u,B)$ is a smooth solutions to Hall-MHD equations satisfying $(u,B)\in L.%\frac{9}{2}(\mathbb{R}.3)$,then we have $u=B=0$. This improves a recent result of Chae et al. [2] and Zujin et al. [14].


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    [2] D. Chae, P. Degond and J.G. Liu, Well-posedness for Hall-magnetohydrodynamics, Ann. Inst. H. Poincar´e Anal. Non Lin´eaire, 31 (2014), 555-565
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    [8] G.P. Galdi, An Introduction to the Mathematical Theory of the Navier–Stokes Equations, Steady State Problems. 2nd Edition, Springer Monographs in Mathematics, Springer, NewYork, 2011.
    [9] F. He, B. Ahmad, T. Hayat and Y. Zhou, On regularity criteria for the 3D Hall-MHD equations in terms of the velocity, Nonlinear Anal. Real World Appl., 32 (2016), 35-51.
    [10] Y. Zhuan, Regulatity criterion for the 3D Hall-magnetohydrodynamic equations involing the vorticity, Nonlinear Anal. 144 (2016), 182-193.
    [11] Y. Zhuan, Regulatity criteria and small data global existence to the generalized viscous Hallmagnetohydrodynamics, Comput. Math. Appl., 70 (2015), 2137-2154.
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    [13] R. Wan and Y. Zhou, Yong Low regularity well-posedness for the 3D generalized Hall-MHD system, To appear in Acta Appl. Math., DOI: 10.1007/s10440-016-0070-5.
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  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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