Unconditional well-posedness in the energy space for the Ginzburg-Landau equation

2019 ◽  
Author(s):  
Elena Nikolova ◽  
Mirko Tarulli ◽  
George Venkov
Keyword(s):  
Landau Equation ◽  
Energy Space ◽  
Well Posedness ◽  
Ginzburg Landau ◽  
Ginzburg Landau Equation

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

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.

Well-posedness for the nonlinear fractional Schrödinger equation and inviscid limit behavior of solution for the fractional Ginzburg-Landau equation

2013 ◽  
Vol 16 (1) ◽  
Author(s):  
Boling Guo ◽  
Zhaohui Huo
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Landau Equation ◽  
Inviscid Limit ◽  
Well Posedness ◽  
Ginzburg Landau ◽  
Fractional Schrödinger Equation ◽  
Ginzburg Landau Equation ◽  
Nonlinear Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation

AbstractThe well-posedness for the Cauchy problem of the nonlinear fractional Schrödinger equation $u_t + i( - \Delta )^\alpha u + i|u|^2 u = 0,(x,t) \in \mathbb{R}^n \times \mathbb{R},\frac{1} {2} < \alpha < 1 $ is considered. The local well-posedness in subcritical space H s with s > n/2 -α is obtained. Moreover, the inviscid limit behavior of solution for the fractional Ginzburg-Landau equation $u_t + (\nu + i)( - \Delta )^\alpha u + i|u|^2 u = 0$ is also considered. It is shown that the solution of the fractional Ginzburg-Landau equation converges to the solution of nonlinear fractional Schrödinger equation in the natural space C([0, T];H)s) with s > n/2 — α if ν tends to zero.

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