Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 12
209
Views
6
CrossRef citations to date
0
Altmetric
Articles

Refined regularity criteria for the MHD system involving only two components of the solution

Pages 2130-2139 | Received 17 Feb 2016, Accepted 20 Jun 2016, Published online: 11 Jul 2016

References

  • Duvaut G, Lions JL. Inéquations en thermoélasticité et magnétohydrodynamique. Arch. Rational Mech. Anal. 1972;46:241–279. Available from: http://link.springer.com/article/10.1007\%2FBF00250512.
  • Cao CS, Wu JH. Two regularity criteria for the 3D MHD equations. J. Differ. Equ. 2010;248:2263–2274.
  • Chen QL, Miao CX, Zhang ZF. On the regularity criterion of weak solutions for the 3D viscous magneto-hydrodynamics equations. Commun. Math. Phys. 2008;284:919–930.
  • Duan HL. On regularity criteria in terms of pressure for the 3D viscous MHD equations. Appl. Anal. 2012;91: 947–952.
  • He C, Xin ZP. On the regularity of weak solutions to the magnetohydrodynamic equations. J. Differ. Equ. 2005;213:235–254.
  • Ji E, Lee J. Some regularity criteria for the 3D incompressible magnetohydrodynamics. J. Math. Anal. Appl. 2010;369:317–322.
  • Jia XJ. A new scaling invariant regularity criterion for the 3D MHD equations in terms of horizontal gradient of horizontal components. Appl. Math. Lett. 2015;50:1–4.
  • Jia XJ, Zhou Y. Ladyzhenskaya-Prodi-Serrin type regularity criteria for the 3D incompressible MHD equations in terms of 3 x 3 mixture matrices. Nonlinearity. 2015;28:3289–3307.
  • Jia XJ, Zhou Y. On regularity criteria for the 3D incompressible MHD equations involving one velocity component. J. Math. Fluid Mech. 2015. doi:10.1007/s00021-015-0246-1.
  • Jia XJ, Zhou Y. Regularity criteria for the 3D MHD equations involving partial components. Nonlinear Anal.: Real World Appl. 2012;13:410–418.
  • Ni LD, Guo ZG, Zhou Y. Some new regularity criteria for the 3D MHD equations. J. Math. Anal. Appl. 2012;396:108–118.
  • Yamazaki K. Regularity criteria of MHD system involving one velocity and one current density component. J. Math. Fluid Mech. 2014;16:551–570.
  • Yamazaki K. Regularity criteria of the three-dimensional MHD system involving one velocity and one vorticity component. Nonlinear Anal. 2016;135:78–83.
  • Zhang ZJ. Remarks on the global regularity criteria for the 3D MHD equations via two components. Z. Angew. Math. Phys. 2015;66:977–987.
  • Zhang ZJ. Regularity criteria for the 3D MHD equations involving one current density and the gradient of one velocity component. Nonlinear Anal. 2015;115:41–49.
  • Zhou Y. Remaks on regularities for the 3D MHD equations. Discrete Cont. Dyn. Syst. 2005;12:881–886.
  • Zhou Y, Fan JS. Logarithmically improved regularity criteria for the 3D viscous MHD equations. Forum Math. 2012;24:691–708.
  • Zhang ZJ, Yao ZA, Lu M, Ni LD. Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations. J. Math. Phys. 2011;52:053103.
  • Chemin JY, Zhang P. On the critical one component regularity for 3-D Navier-Stokes system. Ann. sci. \’{E}c. Norm. Sup\’{e}r. 2016;49:131–167.
  • Yamazaki K. On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces. Bull. Sci. Math. 2016;140:575–614.
  • Sermange M, Temam R. Some mathematical questions realted to the MHD equations. Commun. Pure Appl. Math. 1983;36:635–664.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.