Remarks on the global regularity criteria for the 3D MHD equations via two components

In this paper, we would like to improve the recent results of Yamazaki on the regularity criteria for the three-dimensional magentohydrodynamic equations (Yamazaki in J Math Phys 55:031505, 2014; J Math Fluid Mech. 2014. doi:10.1007/s00021-014-0178-1).

[1]  Zujin Zhang.  Remarks on the regularity criteria for generalized MHD equations , 2011 .

[2]  Chongsheng Cao,et al.  Two regularity criteria for the 3D MHD equations , 2009, 0903.2577.

[3]  J. L. Lions,et al.  Inéquations en thermoélasticité et magnétohydrodynamique , 1972 .

[4]  Yong Zhou,et al.  Some new regularity criteria for the 3D MHD equations , 2012 .

[5]  Zhouping Xin,et al.  On the regularity of weak solutions to the magnetohydrodynamic equations , 2005 .

[6]  J. Kwon,et al.  The twisted Daehee numbers and polynomials , 2014 .

[7]  Jihoon Lee,et al.  Some regularity criteria for the 3D incompressible magnetohydrodynamics , 2010 .

[8]  Yong Zhou,et al.  A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field , 2010 .

[9]  Qionglei Chen,et al.  On the Regularity Criterion of Weak Solution for the 3D Viscous Magneto-Hydrodynamics Equations , 2007, 0711.0123.

[10]  Gaohang Yu,et al.  Regularity criteria for the 3D MHD equations via one directional derivative of the pressure , 2013 .

[11]  Yong Zhou,et al.  Logarithmically improved regularity criteria for the 3D viscous MHD equations , 2012 .

[12]  K. Burazin,et al.  Estimates for mild solutions to semilinear Cauchy problems , 2014 .

[13]  Huiling Duan.  On regularity criteria in terms of pressure for the 3D viscous MHD equations , 2012 .

[14]  Yong Zhou,et al.  Remarks on regularities for the 3D MHD equations , 2005 .

[15]  Kazuo Yamazaki,et al.  Regularity Criteria of MHD System Involving One Velocity and One Current Density Component , 2014 .

[16]  Yong Zhou,et al.  On the regularity of the solutions of the Navier–Stokes equations via one velocity component , 2010 .

[17]  Yong Zhou,et al.  A new regularity criterion for the 3D incompressible MHD equations in terms of one component of the gradient of pressure , 2012 .

[18]  K. Yamazaki.  Remarks on the regularity criteria of three-dimensional magnetohydrodynamics system in terms of two velocity field components , 2014 .

[19]  Roger Temam,et al.  Some mathematical questions related to the MHD equations , 1983 .

[20]  Yong Zhou,et al.  Regularity criteria for the 3D MHD equations involving partial components , 2012 .

[21]  Yong Zhou,et al.  Regularity criteria for the 3D MHD equations via partial derivatives. II , 2012 .