On the Cauchy Problem of the Ginzburg-Landau Equations for Atomic Fermi Gases Near the BCS-BEC Crossover

2009 ◽  
Vol 22 (3) ◽  
pp. 218-233 ◽  
Author(s):  
Chen Shuhong and Guo Boling
Keyword(s):  
Cauchy Problem ◽  
Fermi Gases ◽  
Ginzburg Landau ◽  
The Cauchy Problem ◽  
Ginzburg Landau Equations

scholarly journals A simple approach to the Cauchy problem for complex Ginzburg–Landau equations by compactness methods

2012 ◽  
Vol 253 (4) ◽  
pp. 1250-1263 ◽  
Author(s):  
Philippe Clément ◽  
Noboru Okazawa ◽  
Motohiro Sobajima ◽  
Tomomi Yokota
Keyword(s):  
Cauchy Problem ◽  
Simple Approach ◽  
Ginzburg Landau ◽  
The Cauchy Problem ◽  
Ginzburg Landau Equations

scholarly journals Frequency-Uniform Decomposition, Function Spaces , and Applications to Nonlinear Evolution Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Shaolei Ru ◽  
Jiecheng Chen
Keyword(s):  
Cauchy Problem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Function Spaces ◽  
Nonlinear Evolution Equations ◽  
Ginzburg Landau ◽  
New Class ◽  
The Cauchy Problem ◽  
Ginzburg Landau Equations

By combining frequency-uniform decomposition with (), we introduce a new class of function spaces (denoted by ). Moreover, we study the Cauchy problem for the generalized NLS equations and Ginzburg-Landau equations in .

Cauchy problem for the time-dependent Ginzburg–Landau model of superconductivity

2000 ◽  
Vol 130 (6) ◽  
pp. 1383-1404 ◽  
Author(s):  
A. Rodriguez-Bernal ◽  
B. Wang
Keyword(s):  
Cauchy Problem ◽  
Initial Data ◽  
Existence Result ◽  
Uniqueness Result ◽  
Time Dependent ◽  
Ginzburg Landau ◽  
Landau Model ◽  
The Cauchy Problem ◽  
Ginzburg Landau Equations ◽  
Well Posed

The Cauchy problem for the time-dependent Ginzburg–Landau equations of superconductivity in Rd (d = 2, 3) is investigated in this paper. When d = 2, we show that the Cauchy problem for this model is well posed in L2. When d = 3, we establish the existence result of solutions for L3 initial data and the uniqueness result for L4 initial data.

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