Access the full text.
Sign up today, get DeepDyve free for 14 days.
P. Lemarié–Rieusset (2002)
Recent Developments in the Navier-Stokes Problem
V.G. Maz’ya, T.O. Shaposhnikova (1995)
Theory of multipliers in spaces of differentiable functions, Monographs and Studies in Mathematics 23
Jishan Fan, Song Jiang, Guoxi Ni (2008)
On regularity criteria for the n-dimensional Navier–Stokes equations in terms of the pressureJournal of Differential Equations, 244
Z.J. Zhang, Z.A. Yao, X.F. Wang (2011)
A regularity criterion for the 3D magneto-micropolar fluid equations in Triebel–Lizorkin spacesNonlinear Analysis: TMA, 74
Yong Zhou, S. Gala (2010)
Regularity criteria for the solutions to the 3D MHD equations in the multiplier spaceZeitschrift für angewandte Mathematik und Physik, 61
H. Triebel (1978)
Interpolation Theory, Function Spaces, Differential Operators
J. Beale, Tosio Kato, A. Majda (1984)
Remarks on the breakdown of smooth solutions for the 3-D Euler equationsCommunications in Mathematical Physics, 94
Zujin Zhang, Z. Yao, Xiaofeng Wang (2011)
A regularity criterion for the 3D magneto-micropolar fluid equations in Triebel–Lizorkin spacesNonlinear Analysis-theory Methods & Applications, 74
Y. Du, Y. Liu, Z.A. Yao (2009)
Remarks on the blow-up criteria for 3D ideal magnetohydrodynamic equationsJ. Math. Phys., 50
H. Triebel (1978)
Interpolation theory, function Spaces, differential Operators, North Holland, Amsterdam
V. Maz'ya, T. Shaposhnikova (1983)
Theory of multipliers in spaces of differentiable functionsRussian Mathematical Surveys, 38
Zujin Zhang (2011)
Remarks on the regularity criteria for generalized MHD equationsJournal of Mathematical Analysis and Applications, 375
F. Lin, Chun Liu (1995)
Nonparabolic dissipative systems modeling the flow of liquid crystalsCommunications on Pure and Applied Mathematics, 48
F. Lin (1989)
Nonlinear theory of defects in nematic liquid crystals; Phase transition and flow phenomenaCommunications on Pure and Applied Mathematics, 42
(2005)
Reguarity criteria via two components of vorticity on weak solutions to the Navier-Stokes equations in R3
Zujin Zhang (2010)
Regularity criterion for the system modeling the flow of liquid crystals via the direction of velocity
Yong Zhou, S. Gala (2009)
Logarithmically improved regularity criteria for the Navier–Stokes equations in multiplier spacesJournal of Mathematical Analysis and Applications, 356
Jishan Fan, B. Guo (2008)
Regularity criterion to some liquid crystal models and the Landau-Lifshitz equations in ℝ3Science in China Series A: Mathematics, 51
J.S. Fan, B.L. Guo (2008)
Regularity criterion to some liquid crystal models and the Landau–Lifshitz equations in $${\mathbb{R}^3}$$Chinese Ann Math Ser A., 38
In this paper, we consider the regularity criteria for weak solutions of liquid crystals. It is proved that the solution is in fact smooth if the velocity or the velocity gradient belongs to some critical multiplier spaces or Tribel–Lizorkin spaces. As a corollary, we obtain the Beal–Kato–Majda criteria for liquid crystals.
Journal of Evolution Equations – Springer Journals
Published: Dec 1, 2012
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.