Partial regularity criteria for suitable weak solutions of the three-dimensional liquid crystals flow

2016 ◽  
Vol 39 (14) ◽  
pp. 4196-4207 ◽  
Author(s):  
Huan Yu
Keyword(s):  
Liquid Crystals ◽  
Weak Solutions ◽  
Partial Regularity ◽  
Three Dimensional ◽  
Regularity Criteria ◽  
Suitable Weak Solutions

scholarly journals Partial regularity of suitable weak solutions to the multi-dimensional generalized magnetohydrodynamics equations

2016 ◽  
Vol 18 (06) ◽  
pp. 1650018 ◽  
Author(s):  
Wei Ren ◽  
Yanqing Wang ◽  
Gang Wu
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Morrey Space ◽  
Stokes Equations ◽  
Mhd Equations ◽  
Regularity Criteria ◽  
Navier Stokes ◽  
Mixed Norm ◽  
Suitable Weak Solutions ◽  
Navier Stokes Equations

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in [Formula: see text] for [Formula: see text]. In comparison with the work of the 3D fractional Navier–Stokes equations obtained by Tang and Yu in [Partial regularity of suitable weak solutions to the fractional Navier–Stokes equations, Comm. Math. Phys. 334 (2015) 1455–1482], our results include their endpoint case [Formula: see text] and the external force belongs to a more general parabolic Morrey space. Moreover, we prove some interior regularity criteria just via the scaled mixed norm of the velocity for the suitable weak solutions to the fractional MHD equations.

Remarks on regularity criteria for the weak solutions of liquid crystals

2012 ◽  
Vol 12 (4) ◽  
pp. 801-812 ◽  
Author(s):  
Zujin Zhang ◽  
Xiaofeng Wang ◽  
Zheng-an Yao
Keyword(s):  
Liquid Crystals ◽  
Weak Solutions ◽  
Regularity Criteria
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