Uniqueness of weak solutions in critical space of the 3-D time-dependent Ginzburg-Landau equations for superconductivity

2010 ◽  
Vol 283 (8) ◽  
pp. 1134-1143 ◽  
Author(s):  
Jishan Fan ◽  
Hongjun Gao
Keyword(s):  
Weak Solutions ◽  
Time Dependent ◽  
Critical Space ◽  
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.

Geometric effect on the vortex configuration and motion in mesoscopic superconducting cylinders

2015 ◽  
Vol 29 (03) ◽  
pp. 1550009 ◽  
Author(s):  
Shan-Shan Wang ◽  
Guo-Qiao Zha
Keyword(s):  
Phase Transitions ◽  
Vortex Dynamics ◽  
Axial Symmetry ◽  
Time Dependent ◽  
Vortex Matter ◽  
Ginzburg Landau ◽  
Geometric Effect ◽  
Multiply Connected ◽  
Vortex States ◽  
Ginzburg Landau Equations

Based on the time-dependent Ginzburg–Landau equations, we study numerically the vortex configuration and motion in mesoscopic superconducting cylinders. We find that the effects of the geometric symmetry of the system and the noncircular multiply-connected boundaries can significantly influence the steady vortex states and the vortex matter moving. For the square cylindrical loops, the vortices can enter the superconducting region in multiples of 2 and the vortex configuration exhibits the axial symmetry along the square diagonal. Moreover, the vortex dynamics behavior exhibits more complications due to the existed centered hole, which can lead to the vortex entering from different edges and exiting into the hole at the phase transitions.

Time-dependent Ginzburg-Landau equations for a dirty gapless superconductor

1985 ◽  
Vol 32 (5) ◽  
pp. 2965-2975 ◽  
Author(s):  
Jerome J. Krempasky ◽  
Richard S. Thompson
Keyword(s):  
Time Dependent ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equations
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