@article{AIHPC_2007__24_3_491_0,
author = {Zhou, Yong},
title = {Regularity criteria for the generalized viscous {MHD} equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {491--505},
year = {2007},
publisher = {Elsevier},
volume = {24},
number = {3},
doi = {10.1016/j.anihpc.2006.03.014},
mrnumber = {2321203},
zbl = {1130.35110},
language = {en},
url = {https://www.numdam.org/articles/10.1016/j.anihpc.2006.03.014/}
}
TY - JOUR AU - Zhou, Yong TI - Regularity criteria for the generalized viscous MHD equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2007 SP - 491 EP - 505 VL - 24 IS - 3 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/j.anihpc.2006.03.014/ DO - 10.1016/j.anihpc.2006.03.014 LA - en ID - AIHPC_2007__24_3_491_0 ER -
%0 Journal Article %A Zhou, Yong %T Regularity criteria for the generalized viscous MHD equations %J Annales de l'I.H.P. Analyse non linéaire %D 2007 %P 491-505 %V 24 %N 3 %I Elsevier %U https://www.numdam.org/articles/10.1016/j.anihpc.2006.03.014/ %R 10.1016/j.anihpc.2006.03.014 %G en %F AIHPC_2007__24_3_491_0
Zhou, Yong. Regularity criteria for the generalized viscous MHD equations. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 3, pp. 491-505. doi: 10.1016/j.anihpc.2006.03.014
[1] , A new regularity class for the Navier-Stokes equations in , Chinese Ann. Math. 16 (1995) 407-412. | Zbl
[2] , Vorticity and smoothness in viscous flows, in: Nonlinear Problems in Mathematical Physics and Related Topics, II, Int. Math. Ser. (N.Y.), vol. 2, Kluwer/Plenum, New York, 2002, pp. 61-67. | MR
[3] , , On the regularizing effect of the vorticity direction in incompressible viscous flows, Differential Integral Equations 15 (3) (2002) 345-356. | Zbl | MR
[4] , , , Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982) 771-831. | Zbl
[5] , , , Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD, Comm. Math. Phys. 184 (2) (1997) 443-455. | Zbl | MR
[6] , Perfect Incompressible Fluids, Oxford Lecture Series in Mathematics and its Applications, vol. 14, The Clarendon Press, Oxford University Press, New York, 1998. | Zbl | MR
[7] , , Direction of vorticity and the problem of global regularity for the Navier-Stokes equations, Indiana Univ. Math. J. 42 (1993) 775-789. | Zbl
[8] , Fourier Analysis, Graduate Studies in Mathematics, vol. 29, American Mathematical Society, Providence, RI, 2001, Translated and revised from the 1995 Spanish original by David Cruz-Uribe. | Zbl | MR
[9] , On partial regularity for weak solutions to the Navier-Stokes equations, J. Funct. Anal. 211 (1) (2004) 153-162. | Zbl
[10] , , On the regularity of solutions to the magnetohydrodynamic equations, J. Differential Equations 213 (2) (2005) 235-254. | Zbl | MR
[11] , , Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math. 36 (5) (1983) 635-664. | Zbl | MR
[12] , On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 9 (1962) 187-195. | Zbl
[13] , Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | Zbl | MR
[14] , , Gradient estimation on Navier-Stokes equations, Comm. Anal. Geom. 7 (1999) 221-257. | Zbl
[15] , Generalized MHD equations, J. Differential Equations 195 (2003) 284-312. | Zbl | MR
[16] , Bounds and new approaches for the 3D MHD equations, J. Nonlinear Sci. 12 (4) (2002) 395-413. | Zbl | MR
[17] , A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component, Method Appl. Anal. 9 (4) (2002) 563-578.
[18] , Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain, Math. Ann. 328 (1-2) (2004) 173-192. | Zbl
[19] , A new regularity criterion for the Navier-Stokes equations in terms of the direction of vorticity, Monatsh. Math. 144 (2005) 251-257. | Zbl
[20] , A new regularity criterion for weak solutions to the Navier-Stokes equations, J. Math. Pures Appl. (9) 84 (11) (2005) 1496-1514. | Zbl
[21] , Remarks on regularities for the 3D MHD equations, Discrete Contin. Dynam. Syst. 12 (5) (2005) 881-886. | Zbl | MR
[22] , On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in , Z. Angew. Math. Phys. 57 (2006) 384-392. | Zbl
Cité par Sources :





