scholarly journals Partial regularity and the Minkowski dimension of singular points for suitable weak solutions to the 3D simplified Ericksen–Leslie system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Qiao Liu
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Singular Points ◽  
Minkowski Dimension ◽  
Suitable Weak Solutions ◽  
Leslie System

On the partial regularity of suitable weak solutions in the non-Newtonian shear-thinning case

Nonlinearity ◽  
2021 ◽  
Vol 34 (1) ◽  
pp. 562-577
Author(s):  
Hugo Beirão da Veiga ◽  
Jiaqi Yang
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Shear Thinning ◽  
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.

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