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Applicable Analysis
An International Journal
Volume 91, 2012 - Issue 5
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Original Articles

On regularity criteria in terms of pressure for the 3D viscous MHD equations

Huiling Duan College of Mathematics and Computer Science, Chongqing Three Gorges University, Wanzhou 404000, Chongqing, P.R. ChinaCorrespondence[email protected]
Pages 947-952 | Received 04 Nov 2010, Accepted 08 Jan 2011, Published online: 21 Mar 2011

References

  • Sermange , M and Temam , R . 1983 . Some mathematical questions related to the MHD equations . Commun. Pure Appl. Math. , 36 ( 5 ) : 635 – 664 .
  • He , C and Xin , Z . 2005 . On the regularity of weak solutions to the magnetohydrodynamic equations . J. Differ. Eqns , 213 : 235 – 254 .
  • Zhou , Y . 2005 . Remarks on regularities for the 3D MHD equations . Discrete Contin. Dyn. Syst. , 12 : 881 – 886 .
  • Chen , Q , Miao , C and Zhang , Z . 2007 . The Beale–Kato–Majda criterion for the 3D magneto-hydrodynamics equations . Commun. Math. Phys. , 275 ( 3 ) : 861 – 872 .
  • He , C and Wang , Y . 2008 . Remark on the regularity for weak solutions to the magnetohydrodynamic equations . Math. Methods Appl. Sci. , 31 ( 14 ) : 1667 – 1684 .
  • Zhou , Y and Gala , S . 2010 . Regularity criteria for the solutions to the 3D MHD equations in the multiplier space . Z. Angew. Math. Phys. , 61 ( 2 ) : 193 – 199 .
  • Wu , J . 2008 . Regularity criteria for the generalized MHD equations . Commun. Partial Differ. Eqns , 33 ( 1–3 ) : 285 – 306 .
  • Zhou , Y . 2006 . Regularity criteria for the 3D MHD equations in terms of the pressure . Int. J. Non-Linear Mech. , 41 ( 10 ) : 1174 – 1180 .
  • Zhou , Y . 2007 . Regularity criteria for the generalized viscous MHD equations . Ann. Inst. H. Poincaré Anal. NonLinéaire , 24 ( 3 ) : 491 – 505 .
  • Zhou , Y and Gala , S . 2010 . A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field . Nonlinear Anal. , 72 ( 9–10 ) : 3643 – 3648 .
  • Fan , J , Jiang , S , Nakamura , G and Zhou , Y . 2011 . Logarithmically improved regularity criteria for the Navier–Stokes and MHD equations . J. Math. Fluid Mech. , (to appear), doi: 10.1007/s00021-010-0039-5
  • Zhou , Y and Fan , J . 2011 . Logarithmically improved regularity criteria for the 3D viscous MHD equations . Forum Math. , (to appear), doi: 10.1515/FORM.2011.079
  • Zhou , Y . 2006 . On regularity criteria in terms of pressure for the Navier–Stokes equations in ℝ3 . Proc. Am. Math. Soc. , 134 : 149 – 156 .
  • Zhou , Y . 2006 . On a regularity criterion in terms of the gradient of pressure for the Navier–Stokes equations in ℝ N . Z. Angew. Math. Phys. , 57 : 384 – 392 .
  • Struwe , M . 2007 . On a Serrin-type regularity criterion for the Navier–Stokes equations in terms of the pressure . J. Math. Fluid Mech. , 9 ( 2 ) : 235 – 242 .

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