no. 3
Regularity criteria for the generalized viscous MHD equations
Zhou, Yong1
1 Chinese University of Hong Kong, Institute of Mathematical Sciences and Department of Mathematics, Shatin, N.T. (Hong Kong), Xiamen University, Xiamen, Fujian (Chine)
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
Zhou, Yong 1

1 Chinese University of Hong Kong, Institute of Mathematical Sciences and Department of Mathematics, Shatin, N.T. (Hong Kong), Xiamen University, Xiamen, Fujian (Chine) 
@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},
     publisher = {Elsevier},
     volume = {24},
     number = {3},
     year = {2007},
     doi = {10.1016/j.anihpc.2006.03.014},
     mrnumber = {2321203},
     zbl = {1130.35110},
     language = {en},
     url = {http://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  - http://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 http://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. http://www.numdam.org/articles/10.1016/j.anihpc.2006.03.014/

[1] Beirão Da Veiga H., A new regularity class for the Navier-Stokes equations in R n , Chinese Ann. Math. 16 (1995) 407-412. | Zbl

[2] Beirão Da Veiga H., 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] Beirão Da Veiga H., Berselli L.C., On the regularizing effect of the vorticity direction in incompressible viscous flows, Differential Integral Equations 15 (3) (2002) 345-356. | MR | Zbl

[4] Caffarelli L., Kohn R., Nirenberg L., Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982) 771-831. | Zbl

[5] Caflisch R., Klapper I., Steele G., Remarks on singularities, dimension and energy dissipation for ideal hydrodynamics and MHD, Comm. Math. Phys. 184 (2) (1997) 443-455. | MR | Zbl

[6] Chemin J.Y., Perfect Incompressible Fluids, Oxford Lecture Series in Mathematics and its Applications, vol. 14, The Clarendon Press, Oxford University Press, New York, 1998. | MR | Zbl

[7] Constantin P., Fefferman C., Direction of vorticity and the problem of global regularity for the Navier-Stokes equations, Indiana Univ. Math. J. 42 (1993) 775-789. | Zbl

[8] Duoandikoetxea J., 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. | MR | Zbl

[9] He C., On partial regularity for weak solutions to the Navier-Stokes equations, J. Funct. Anal. 211 (1) (2004) 153-162. | Zbl

[10] He C., Xin Z., On the regularity of solutions to the magnetohydrodynamic equations, J. Differential Equations 213 (2) (2005) 235-254. | MR | Zbl

[11] Sermange M., Temam R., Some mathematical questions related to the MHD equations, Comm. Pure Appl. Math. 36 (5) (1983) 635-664. | MR | Zbl

[12] Serrin J., On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal. 9 (1962) 187-195. | Zbl

[13] Stein E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Mathematical Series, vol. 30, Princeton University Press, Princeton, NJ, 1970. | MR | Zbl

[14] Tian G., Xin Z., Gradient estimation on Navier-Stokes equations, Comm. Anal. Geom. 7 (1999) 221-257. | Zbl

[15] Wu J., Generalized MHD equations, J. Differential Equations 195 (2003) 284-312. | MR | Zbl

[16] Wu J., Bounds and new approaches for the 3D MHD equations, J. Nonlinear Sci. 12 (4) (2002) 395-413. | MR | Zbl

[17] Zhou Y., 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] Zhou Y., 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] Zhou Y., A new regularity criterion for the Navier-Stokes equations in terms of the direction of vorticity, Monatsh. Math. 144 (2005) 251-257. | Zbl

[20] Zhou Y., A new regularity criterion for weak solutions to the Navier-Stokes equations, J. Math. Pures Appl. (9) 84 (11) (2005) 1496-1514. | Zbl

[21] Zhou Y., Remarks on regularities for the 3D MHD equations, Discrete Contin. Dynam. Syst. 12 (5) (2005) 881-886. | MR | Zbl

[22] Zhou Y., On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in R N , Z. Angew. Math. Phys. 57 (2006) 384-392. | Zbl

Cité par Sources :