Global well-posedness of a stochastic coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection

2012 ◽  
Vol 53 (3) ◽  
pp. 033710 ◽  
Author(s):  
Wei Wu ◽  
Shangbin Cui ◽  
Jinqiao Duan
Keyword(s):  
Marangoni Convection ◽  
Type Model ◽  
Well Posedness ◽  
Ginzburg Landau

On a coupled Kuramoto–Sivashinsky and Ginzburg–Landau-type model for the Marangoni convection

1997 ◽  
Vol 38 (5) ◽  
pp. 2465-2474 ◽  
Author(s):  
Jinqiao Duan ◽  
Charles Bu ◽  
Hongjun Gao ◽  
Mario Taboada
Keyword(s):  
Marangoni Convection ◽  
Type Model ◽  
Ginzburg Landau

scholarly journals Well-posedness of the fractional Ginzburg–Landau equation

2018 ◽  
Vol 98 (14) ◽  
pp. 2545-2558 ◽  
Author(s):  
Xian-Ming Gu ◽  
Lin Shi ◽  
Tianhua Liu
Keyword(s):  
Landau Equation ◽  
Well Posedness ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

scholarly journals Local well-posedness and blow-up for the half Ginzburg-Landau-Kuramoto equation with rough coefficients and potential

2019 ◽  
Vol 39 (5) ◽  
pp. 2661-2678 ◽  
Author(s):  
Luigi Forcella ◽  
◽  
Kazumasa Fujiwara ◽  
Vladimir Georgiev ◽  
Tohru Ozawa ◽  
...  
Keyword(s):  
Blow Up ◽  
Well Posedness ◽  
Ginzburg Landau ◽  
Rough Coefficients

WELL POSEDNESS FOR A PHASE TRANSITION MODEL IN SUPERCONDUCTIVITY WITH VELOCITY AND MAGNETIC CRITICAL FIELDS

2009 ◽  
Vol 19 (01) ◽  
pp. 1-30 ◽  
Author(s):  
V. BERTI ◽  
M. FABRIZIO
Keyword(s):  
Phase Transition ◽  
Thermal Effects ◽  
Transition Model ◽  
Well Posedness ◽  
Threshold Values ◽  
Critical Fields ◽  
Ginzburg Landau ◽  
Fixed Parameter ◽  
Superconducting Current ◽  
The Magnetic Field

In this paper we present a Ginzburg–Landau model to describe the phenomenon of superconductivity as a second-order phase transition. The model proposed, which also includes thermal effects, allows to explain the existence of threshold values, both of the magnetic field and of the superconducting current, beyond which superconductivity vanishes. This is achieved by introducing a constitutive equation for the magnetic induction where the magnetic permeability depends on the complex order parameter. The model is proved to be consistent with thermodynamical principles. The resulting differential system is studied under the assumption that the temperature is a fixed parameter and its well-posedness is proved.

ASYMPTOTIC DYNAMICS OF 2D FRACTIONAL COMPLEX GINZBURG–LANDAU EQUATION

2013 ◽  
Vol 23 (12) ◽  
pp. 1350202 ◽  
Author(s):  
HONG LU ◽  
SHUJUAN LÜ ◽  
ZHAOSHENG FENG
Keyword(s):  
Global Attractor ◽  
Landau Equation ◽  
Fractal Dimensions ◽  
Well Posedness ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation ◽  
Spatial Dimensions ◽  
Asymptotic Dynamics ◽  
Hausdorff And Fractal Dimensions ◽  
The Galerkin Method

In this paper, we consider the well-posedness and asymptotic behaviors of solutions of the fractional complex Ginzburg–Landau equation with the initial and periodic boundary conditions in two spatial dimensions. We explore the existence and uniqueness of global smooth solution by means of the Galerkin method and establish the existence of the global attractor. The estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractor are presented.

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