Partial Regularity of Suitable Weak Solutions of Complex Ginzburg Landau Equations

1999 ◽  
Vol 24 (11-12) ◽  
pp. 390-393
Author(s):  
Xiaodong Yan
Keyword(s):  
Weak Solutions ◽  
Partial Regularity ◽  
Suitable Weak Solutions ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations

Existence of the solutions for the Ginzburg–Landau equations of superconductivity in three spatial dimensions

1999 ◽  
Vol 129 (3) ◽  
pp. 627-639 ◽  
Author(s):  
Bixiang Wang ◽  
Ning Su
Keyword(s):  
Initial Data ◽  
Weak Solutions ◽  
Time Dependent ◽  
Global Weak Solutions ◽  
Ginzburg Landau ◽  
Spatial Dimensions ◽  
Ginzburg Landau Equations

The time-dependent Ginzburg-Landau equations of superconductivity in three spatial dimensions are investigated in this paper. We establish the existence of global weak solutions for this model with any Lp (p ≧ 3) initial data. This work generalizes the results of Wang and Zhan.

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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