Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 96, 2017 - Issue 12
Submit an article Journal homepage
154
Views
6
CrossRef citations to date
0
Altmetric
Articles

A logarithmically improved regularity criterion for the MHD equations in terms of one directional derivative of the pressure

Samia BenbernouFaculté des sciences exactes et appliquées, Département de Mathématiques, Université d’ Oran 1, Oran, Algeria.Correspondence[email protected]
,
Maria Alessandra RagusaDipartimento di Matematica e InformaticaUniversità di Catania, Catania, Italy.
&
Mekki TerbecheFaculté des sciences exactes et appliquées, Département de Mathématiques, Université d’ Oran 1, Oran, Algeria.
Pages 2140-2148 | Received 21 Apr 2016, Accepted 23 Jun 2016, Published online: 25 Jul 2016

References

  • Duvaut G, Lions JL. Inéquations en thermoé lasticité et magnéto-hydrodynamique. Arch. Rational Mech. Anal. 1972;46:241–279.
  • Sermange M, Temam R. Some mathematical questions related to the MHD equations. Commun. Pure Appl. Math. 1983;36:635–664.
  • He C, Xin Z. On the regularity of weak solutions to the magnetohydrodynamic equations. J. Differ. Equ. 2005;213:235–254.
  • Zhou Y. Remarks on regularities for the 3D MHD equations. Discrete Contin. Dyn. Syst. 2005;12:881–886.
  • Zhou Y, Gala S. Regularity criteria for the solutions to the 3D MHD equations in the multiplier space. Z. Angew. Math. Phys. 2010;61:193–199.
  • Zhou Y, Gala S. A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field. Nonlinear Anal. 2010;72:3643–3648.
  • Jia X, Zhou Y. Regularity criteria for the 3D MHD equations involving partial components. Nonlinear Anal. Real World Appl. 2012;13:410–418.
  • Ni L, Guo Z, Zhou Y. Some new regularity criteria for the 3D MHD equations. J. Math. Anal. Appl. 2012;396:108–118.
  • Cao C, Wu J. Two regularity criteria for the 3D MHD equations. J. Differ. Equ. 2010;248:2263–2274.
  • Jia XJ, Zhou Y. A new regularity criterion for the 3D incompressible MHD equations in terms of one component of the gradient of pressure. J. Math. Anal. Appl. 2012;396:345–350.
  • Zhang ZJ, Li P, Yu GH. Regularity criteria for the 3D MHD equations via one directional derivative of the pressure. J. Math. Anal. Appl. 2013;401:66–71.
  • Duan HL. On regularity criteria in terms of pressure for the 3D viscous MHD equations. Appl. Anal. 2012;91:947–952.
  • Fan J, Jiang S, Nakamura G, et al. Logarithmically improved regularity criteria for the Navier--Stokes and MHD equations. J. Math. Fluid Mech. 2011;13:5576571.
  • Jia X, Zhou Y. Regularity criteria for the 3D MHD equations via partial derivatives. Kinet. Relat. Models. 2012;5:505–516.
  • Zhou Y. Regularity criteria for the 3D MHD equations in terms of the pressure. Int. J. Non-Linear Mech. 2006;41:1174–1180.
  • Zhou Y, Fan J. Logarithmically improved regularity criteria for the 3D viscous MHD equations. Forum Math. 2012;24:691–708.
  • Gala S. Extension criterion on regularity for weak solutions to the 3D MHD equations. Math. Methods Appl. Sci. 2010;33:1496–1503.
  • He C, Wang Y. Remark on the regularity for weak solutions to the magnetohydrodynamic equations. Math. Methods Appl. Sci. 2008;31:1667–1684.
  • Mahalov A, Nicolaenko B, Shilkin T. L3,α solutions to the MHD equations. J. Math. Sci. 2007;143:2911–2923.

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.