`a`
Kinetic and Related Models (KRM)
 

Regularity criteria for the 3D MHD equations via partial derivatives. II
Pages: 291 - 304, Issue 2, June 2014

doi:10.3934/krm.2014.7.291      Abstract        References        Full text (407.9K)           Related Articles

Xuanji Jia - Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China (email)
Yong Zhou - Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China (email)

1 L. Berselli and G. Galdi, Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations, Proc. Amer. Math. Soc., 130 (2002), 3585-3595.       
2 C. Cao and E. Titi, Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor, Arch. Ration. Mech. Anal., 202 (2011), 919-932.       
3 C. Cao and J. Wu, Two regularity criteria for the 3D MHD equations, J. Differential Equations, 248 (2010), 2263-2274.       
4 Q. Chen, C. Miao and Z. Zhang, On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations, Comm. Math. Phys., 284 (2008), 919-930.       
5 H. Duan, On regularity criteria in terms of pressure for the 3D viscous MHD equations, Appl. Anal., 91 (2012), 947-952.       
6 G. Duvaut and J. Lions, Inéquations en thermoélasticité et magnétohydrodynamique, Arch. Ration. Mech. Anal., 46 (1972), 241-279.       
7 C. He and Z. Xin, On the regularity of weak solutions to the magnetohydrodynamic equations, J. Differential Equations, 213 (2005), 235-254.       
8 E. Ji and J. Lee, Some regularity criteria for the 3D incompressible magnetohydrodynamics, J. Math. Anal. Appl., 369 (2010), 317-322.       
9 X. Jia and Y. Zhou, Regularity criteria for the 3D MHD equations via partial derivatives, Kinet. Relat. Models, 5 (2012), 505-516.       
10 X. Jia and Y. Zhou, A new regularity criterion for the 3D incompressible MHD equations in terms of one component of the gradient of pressure, J. Math. Anal. Appl., 396 (2012), 345-350.       
11 H. Lin and L. Du, Regularity criteria for incompressible magnetohydrodynamics equations in three dimensions, Nonlinearity, 26 (2013), 219-239.       
12 M. Sermange and R. Temam, Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math., 36 (1983), 635-664.       
13 F. Wang and K. Wang, Global existence of 3D MHD equations with mixed partial dissipation and magnetic diffusion, Nonlinear Anal. Real World Appl., 14 (2013), 526-535.       
14 J. Wu, Viscous and inviscid magnetohydrodynamics equations, J. Anal. Math., 73 (1997), 251-265.       
15 J. Wu, Bounds and new approaches for the 3D MHD equations, J. Nonlinear Sci., 12 (2002), 395-413.       
16 J. Wu, Regularity results for weak solutions of the 3D MHD equations, Discrete Contin. Dyn. Syst., 10 (2004), 543-556.
17 K. Yamazaki, Remarks on the regularity criteria of generalized MHD and Navier-Stokes systems, J. Math. Phys., 54 (2013), 011502, 16pp.       
18 Z. Zhang, Z. Yao, M. Lu and L. Ni, Some Serrin-type regularity criteria for weak solutions to the Navier-Stokes equations, J. Math. Phys., 52 (2011), 053103, 7 pp.       
19 Z. Zhang, P. Li and G. Yu, Regularity criteria for the 3D MHD equations via one directional derivative of the pressure, J. Math. Anal. Appl., 401 (2013), 66-71.       
20 Y. Zhou, Remarks on regularities for the 3D MHD equations, Discrete Contin. Dyn. Syst., 12 (2005), 881-886.       
21 Y. Zhou, Regularity criteria for the 3D MHD equations in terms of the pressure, Int. J. Non-Linear Mech., 41 (2006), 1174-1180.       
22 Y. Zhou, On regularity criteria in terms of pressure for the Navier-Stokes equations in $\mathbbR^3$, Proc. Amer. Math. Soc., 134 (2006), 149-156.       
23 Y. Zhou, On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in $\mathbbR^N$, Z. Angew. Math. Phys., 57 (2006), 384-392.       

Go to top