zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
An improved regularity criterion of three-dimensional magnetohydrodynamic equations. (English) Zbl 1239.76070
Summary: An improved regularity criterion for a weak solution of three-dimensional magnetohydrodynamic equations is obtained. Employing the Fourier localization technique, it is proved that weak solutions become regular on (0,T] if the summation of velocity field u and magnetic field b belong to the largest critical spaces: u+bL 2 1+r (0,T;(B , r ( 3 )), -1<r1. This obviously extends the previous results.
76W05Magnetohydrodynamics and electrohydrodynamics
35Q35PDEs in connection with fluid mechanics
76M25Other numerical methods (fluid mechanics)
[1]Sermange, M.; Teman, R.: Some mathematical questions related to the MHD equations, Comm. pure appl. Math. 36, 635-664 (1983) · Zbl 0524.76099 · doi:10.1002/cpa.3160360506
[2]He, C.; Xin, Z.: On the regularity of solutions to the magnetohydrodynamic equations, J. differential equations 213, 235-254 (2005) · Zbl 1072.35154 · doi:10.1016/j.jde.2004.07.002
[3]Zhou, Y.: Remarks on regularities for the 3D MHD equations, Discrete contin. Dyn. syst. 12, 881-886 (2005) · Zbl 1068.35117 · doi:10.3934/dcds.2005.12.881
[4]Chen, Q.; Miao, C.; Zhang, Z.: On the regularity criterion of weak solution for the 3D viscous magneto-hydrodynamics equations, Comm. math. Phys. 284, 919-930 (2008) · Zbl 1168.35035 · doi:10.1007/s00220-008-0545-y
[5]Chen, Q.; Miao, C.; Zhang, Z.: The beale–Kato–majda criterion for the 3D magneto-hydrodynamics equations, Comm. math. Phys. 275, 861-872 (2007) · Zbl 1138.76066 · doi:10.1007/s00220-007-0319-y
[6]He, C.; Wang, Y.: On the regularity criteria for weak solutions to the magnetohydrodynamic equations, J. differential equations 238, 1-17 (2007) · Zbl 1220.35117 · doi:10.1016/j.jde.2007.03.023
[7]Cao, C.; Wu, J.: Two regularity criteria for the 3D MHD equations, J. differential equations 248, 2263-2274 (2010)
[8]Zhou, Y.; Gala, S.: Regularity criteria for the solutions to the 3D MHD equations in the multiplier space, Z. angew. Math. phys. 61, 193-199 (2010)
[9]Zhou, Y.; Gala, S.: A new regularity criterion for weak solutions to the viscous MHD equations in terms of the vorticity field, Nonlinear anal. TMA 72, 3643-3648 (2010) · Zbl 1185.35204 · doi:10.1016/j.na.2009.12.045
[10]Hasegawa, A.: Self-organization processes in continuous media, Adv. phys. 34, 1-42 (1985)
[11]Politano, H.; Pouquet, A.; Sulem, P. L.: Current and vorticity dynamics in three-dimensional magnetohydrodynamics turbulence, Phys. plasmas 2, 2931-2939 (1995)
[12]He, C.; Wang, Y.: Remark on the regularity for weak solutions to the magnetohydrodynamic equations, Math. methods appl. Sci. 31, 1667-1684 (2008) · Zbl 1153.35064 · doi:10.1002/mma.992
[13]Lemarié-Rieusset, P. G.: Recent developments in the Navier–Stokes problem, (2002)
[14]Gala, S.: Extension criterion on regularity for weak solutions to the 3D MHD equations, Math. methods appl. Sci. 33, 1496-1503 (2010) · Zbl 1194.35325 · doi:10.1002/mma.1263
[15]Chemin, J. -Y.: Perfect incompressible fluids, (1998)
[16]Bony, J. -M.: Calcul symbolique et propagation des singulariteś pour LES equations aux deŕiveés partielles non lineáires, Ann. sci. Éc. norm. Supér. 14, 209-246 (1991) · Zbl 0495.35024 · doi:numdam:ASENS_1981_4_14_2_209_0
[17]Triebel, H.: Theory of function spaces, (1983) · Zbl 0546.46027