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.

scholarly journals On the Cauchy problem for the 1+2 complex Ginzburg-Landau equation

1995 ◽  
Vol 36 (3) ◽  
pp. 313-324 ◽  
Author(s):  
Charles Bu
Keyword(s):  
Cauchy Problem ◽  
Global Existence ◽  
Analytical Methods ◽  
Critical Case ◽  
Landau Equation ◽  
Local Existence ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Spatial Dimensions ◽  
The Cauchy Problem

AbstractWe present analytical methods to investigate the Cauchy problem for the complex Ginzburg-Landau equation u1 = (v + iα)Δu − (κ + iβ) |u|2qu + γu in 2 spatial dimensions (here all parameters are real). We first obtain the local existence for v > 0, κ ≥ 0. Global existence is established in the critical case q = 1. In addition, we prove the global existence when .

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