Existence of suitable weak solutions of complex Ginzburg–Landau equations and properties of the set of singular points

2003 ◽  
Vol 44 (11) ◽  
pp. 5185-5193 ◽  
Author(s):  
Xiaofeng Liu ◽  
Houyu Jia
Keyword(s):  
Weak Solutions ◽  
Singular Points ◽  
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.

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

Sign in / Sign up

Export Citation Format

Share Document